Handbook of Quantitative Finance and Risk Management

The main purpose of this chapter is to explore important finance theories. First, we discuss discounted cash-flow valuation theory (classical financial theory). Second, we discuss the Modigliani and Miller (M and M) valuation theory. Third, we examine Markowitz portfolio theory. We then move on to the capital asset pricing model (CAPM), followed by the arbitrage pricing theory. Finally, we will look at the option pricing theory and futures valuation and hedging.

The purpose of this chapter is to discuss the interaction between investment, financing, and dividends policy of the firm. A brief introduction of the policy framework of finance is provided in Sect.

2.1

. Section

2.2

discusses the interaction between investment and dividends policy. Section

2.3

discusses the interaction between dividends and financing policy. Section

2.4

discusses the interaction between investment and financing policy. Section

2.5

discusses the implications of financing and investment interactions for capital budgeting. Section

2.6

discusses the implications of different policies on the beta coefficients. The conclusion is presented in Sect.

2.7

.

The main purpose of this chapter is to discuss important quantitative methods used to do the research in quantitative finance and risk management. We first discuss statistics theory and methods. Second, we discuss econometric methods. Third, we discuss mathematics. Finally, we discuss other methods such as operation research, stochastic process, computer science and technology, entropy, and fuzzy set theory.

In this chapter, we first define the basic concepts of risk and risk measurement. Using the relationship of risk and return, we introduce the efficient-portfolio concept and its implementation. Then the concept of dominance principle and performance measures are also discussed and illustrated. Finally, the interest rate and market rate of return are used as measurements to show how the commercial lending rate and the market risk premium can be calculated.

In this chapter, we first introduce utility function and indifference curve. Based on utility theory, we derive the Markowitz’s model and the efficient frontier through the creation of efficient portfolios of varying risk and return. We also include methods of solving for the efficient frontier both graphically and mathematically, with and without explicitly incorporating short selling.

In this chapter, using the concepts of portfolio analysis and the dominance principle, we derive the capital asset pricing model (CAPM). Then we show how total risk can be decomposed into systematic risk and unsystematic risk. Finally, we discuss the determination of beta and introduce different methods for forecast beta coefficient.

In this chapter, we discuss both the single-index model and multiple-index portfolio selection model. We use constrained maximization instead of minimization procedure to calculate the portfolio weights. We find that both single-index and multi-index models can be used to simplify the Markowitz model for portfolio section.

In this chapter, following Elton et al. (Journal of Finance 31:1341–57, 1976; Modern portfolio theory and investment analysis, 7th edn. Wiley, New York, 2006), we introduce the performance-measure approaches to determine optimal portfolios. We find that the performance-measure approaches for optimal portfolio selection are complementary to the Markowitz full variance-covariance method and the Sharpe index-model method. The economic rationale of the Treynor method is also discussed in detail.

Persistent divergence of an asset price from its fundamental value has been a subject of much theoretical and empirical discussion. This paper takes an alternative approach of inquiry – that of using laboratory experiments – to study the creation and control of speculative bubbles. The following three factors are chosen for analysis: the compensation scheme of portfolio managers, wealth and supply constraints, and the relative risk aversion of traders. Under a short investment horizon induced by a tournament compensation scheme, speculative bubbles are observed in markets of speculative traders and in mixed markets of conservative and speculative traders. These results maintain with super-experienced traders who are aware of the presence of a bubble. A binding wealth constraint dampens the bubbles as does an increased supply of securities. These results are unchanged when traders risk their own money in lieu of initial endowments provided by the experimenter.

In this chapter we introduce the theory and the application of the computer program of modern portfolio theory. The notion of diversification is age-old: “don’t put your eggs in one basket,” obviously predates economic theory. However, a formal model showing how to make the most of the power of diversification was not devised until 1952, a feat for which Harry Markowitz eventually won the Nobel Prize in economics. Markowitz portfolio shows that as you add assets to an investment portfolio the total risk of that portfolio – as measured by the variance (or standard deviation) of total return – declines continuously, but the expected return of the portfolio is a weighted average of the expected returns of the individual assets. In other words, by investing in portfolios rather than in individual assets, investors could lower the total risk of investing without sacrificing return. In the second part we introduce the mean–variance spanning test that follows directly from the portfolio optimization problem.

Securities selection is the attempt to distinguish prospective winners from losers – conditional on beliefs and available information. This article surveys some relevant academic research on the subject, including work about the combining of forecasts (Operational Research Quarterly 20, 451–468, 1969), the Black-Litterman model (Journal of Fixed Income 1(2), 7–18, 1991; Financial Analysts Journal (September/October) 28–43, 1992), the combining of Bayesian priors and regression estimates (Journal of Finance 55(1), 179–223, 2000), model uncertainty and Bayesian model averaging (Statistical Science 14(4), 382–417, 1999; Review of Financial Studies 15(4), 1223–1249, 2002), the theory of competitive storage (Review of Economic Studies 59, 1–23, 1992), and the combination of valuation estimates (Review of Accounting Studies 12(2–3), 227–256, 2007). Despite its wide-ranging applicability, the Bayesian approach is not a license for data snooping. The second half of this article describes common pitfalls in fundamental analysis and comments on the role of theoretical guidance in mitigating these pitfalls.

Previous studies show that combining a power utility portfolio selection model with the empirical probability assessment approach (EPAA) to estimate the joint return distribution frequently generates economically and statistically significant abnormal returns. In this paper, we examine additional ways of estimating joint return distributions that allow us to explore the stationary/nonstationary tradeoffs implicit in “expanding” versus “moving” window estimation methods; the benefits of alternative methods of allowing for the “memory loss” inherent in the moving-window EPAA; and the possibility that weighting more recent observations more heavily may improve investment performance.

This paper investigates the impact of various investment constraints on the benefits and asset allocation of the international optimal portfolio for domestic investors in various countries. The empirical results indicate that local investors in less-developed countries, particularly in East Asia and Latin America, benefit more from global diversification. Although the global financial market is becoming more integrated, adding constraints reduces but does not completely eliminate the diversification benefits of international investment. The addition of portfolio bounds yields the following characteristics of asset allocation: a reduction in the temporal deviation of diversification benefits, a decrease in time-variation of components in optimal portfolio, and an expansion in the range of comprising assets. Our findings are useful for asset management professionals to determine target markets to promote the sales of national/international funds and to manage risk in global portfolios.

Due to limited numbers of reliable international equity funds, the Markowitz investment model is ideal in constructing an international portfolio. Overinvestment in one or several fast-growing markets can be disastrous as political instability and exchange rate fluctuations reign supreme. We apply the Le Châtelier principle to the international equity fund market with a set of upper limits. Tracing out a set of efficient frontiers, we inspect the shifting phenomenon in the mean–variance space. The optimum investment policy can be easily implemented and risk minimized.

We consider the problem of constructing a portfolio of finitely many assets whose return rates are described by a discrete joint distribution. We present a new approach to portfolio selection based on stochastic dominance. The portfolio return rate in the new model is required to stochastically dominate a random benchmark. We formulate optimality conditions and duality relations for these models and construct equivalent optimization models with utility functions. Two different formulations of the stochastic dominance constraint: primal and inverse, lead to two dual problems that involve von Neuman–Morgenstern utility functions for the primal formulation and rank dependent (or dual) utility functions for the inverse formulation. The utility functions play the roles of Lagrange multipliers associated with the dominance constraints. In this way our model provides a link between the expected utility theory and the rank dependent utility theory. We also compare our approach to models using value at risk and conditional value at risk constraints. A numerical example illustrates the new approach.

In 1952, Harry M. Markowitz published a seminal paper about analyzing portfolios. In 1990, he was awarded the Nobel Prize for his portfolio theory. Markowitz portfolio analysis delineates a set of highly desirable investment portfolios. These optimal portfolios have the maximum return at each plausible level of risk, computed iteratively over a range of different risk levels. Conversely, Markowitz portfolio analysis can find the same set of optimal investments by delineating portfolios that have the minimum risk over a range of different rates of return. The set of all Markowitz optimal portfolios is called the efficient frontier. Portfolio analysis analyzes rate of return statistics, risk statistics (standard deviations), and correlations from a list of candidate investments (stocks, bonds, and so on) to determine which investments, and in what proportions (weights), enter into every efficient portfolio. Further analysis of Markowitz’s portfolio theory reveals interesting asset pricing implications.

This chapter is focused on the “Portfolio Theory” created by Markowitz. This theory has the objective of finding the optimum portfolio for investors; that is, that which gives tangency between an indifference curve and the efficient frontier. In this chapter, the mathematics of this model is developed. The CAPM, based on this theory, gives the expected return on an asset depending on the systematic risk of the asset. This model detects underpriced and overpriced assets. The critics expressed against the model and their application possibilities are also analyzed. Finally, the chapter centers on performance measures related to portfolio theory (classic indices, derivative indices and new approaches) and on the performance persistence phenomenon employing the aforementioned indices, including an empirical example.

Intertemporal equilibrium models of the kind discussed in (Asset pricing, Princeton University Press, Princeton, 2001) have become the standard paradigm in most advanced asset pricing courses. The purpose of this chapter is to explain the relationship between this paradigm and the portfolio theory paradigm common in most of the prior asset pricing literature. We show that these paradigms are merely different ways of looking at the same economic phenomena, and that insights can be gained from each approach.

We use a model of stock price behavior in which the expected rate of return on stocks follows an Ornstein- Uhlenbeck process to show that levels of return predictability that cause large variation in valuation ratios and offer significant benefits to dynamic portfolio strategies are hard to detect or measure by standard regression techniques, and that the

R

2

from standard short run predictive regressions carry little information about either long run predictability or the value of dynamic portfolio strategies. We propose a new approach to portfolio planning that uses forward-looking estimates of

long run

expected rates of return from dividend discount models. We show how such long run expected rates of return can be used to estimate the instantaneous expected rate of return under the assumption that the latter follows an Ornstein-Uhlenbeck process. Simulation results using four different estimates of long run rates of return on U.S. common stocks suggest that this approach may be valuable for long horizon investors.

A portfolio insurance strategy is a dynamic hedging process that provides the investor with the potential to limit downside risk while allowing participation on the upside so as to maximize the terminal value of a portfolio over a given investment horizon. First, this paper introduces the basic concepts and payoffs of a portfolio insurance strategy. Second, it describes the theory of alternative portfolio insurance strategies. Third, it empirically compares the performances of various portfolio insurance strategies during different markets and time periods. Fourth, it summaries the recent market developments of portfolio insurance strategies, especially in terms of the variations of features in CPPI investments. Finally, it addresses the impacts of these strategies on financial market stability.

The Capital Asset Pricing Model describes a frictionless world characterized by infinite liquidity. In contrast, trading in an actual marketplace is replete with costs, blockages, and other impediments. Equity market microstructure focuses on how orders are handled and turned into trades in the non-frictionless environment. For over three decades, the literature has grown while, concurrently, trading systems around the world have been reengineered. After depicting the frictionless CAPM, we consider the development of microstructure analysis, concentrating on issues germane to market architecture. We then consider the design of one facility, Deutsche Börse’s electronic platform, Xetra. Important insights were gained from the microstructure literature during Xetra’s planning period (1994–1997), and Xetra’s implementation marked a huge step forward for Germany’s equity markets. Nevertheless, academic research and the design of a real world marketplace remain works in progress.

In this chapter we introduce different types of options and their characteristics. Then, we develop put-call parity theorems for European, American, and futures options. Finally, we discuss option strategies and their investment applications.

In this chapter, we introduce the basic concepts of call and put options. Second, we discuss the Black-Scholes option pricing model and its application. Third, we discuss how to apply the option pricing theory in capital structure issue. Finally, the warrant, one type of equity options, is discussed in detail.

In this chapter, we first introduce the basic concepts of call and put options. Then we show how the simple one period binominal call option pricing model can be derived. Finally, we show how a generalized binominal option pricing model can be derived.

In this chapter, we extend the binomial option pricing model to a multinomial option pricing model. Then we derive the multinomial option pricing model and apply it to the limiting case of Black and Scholes model. Finally, we introduce a lattice framework for option pricing model and its application to option valuation.

In this chapter, we review two famous models on binomial option pricing, Rendleman and Barter (RB 1979) and Cox et al. (CRR 1979). We show that the limiting results of the two models both lead to the celebrated Black-Scholes formula. From our detailed derivations, CRR is easy to follow if one has the advanced level knowledge in probability theory but the assumptions on the model parameters make its applications limited. On the other hand, RB model is intuitive and does not require higher level knowledge in probability theory. Nevertheless, the derivations of RB model are more complicated and tedious. For readers who are interested in the binomial option pricing model, they can compare the two different approaches and find the best one that fits their interests and is easier to follow.

In this chapter, we first introduce normal distribution, lognormal distribution, and their relationship. Then we discuss multivariate normal and lognormal distributions. Finally, we apply both normal and lognormal distributions to derive Black-Scholes formula under the assumption that the rate of stock price follows a lognormal distribution.

The main purpose of this chapter is to present the American option pricing model on stock with dividend payment and without dividend payment. A Microsoft Excel program for evaluating this American option pricing model is also presented.

This paper compares the American option prices with one known dividend under two alternative specifications of the underlying stock price: displaced log normal and log normal processes. Many option pricing models follow the standard assumption of the Black–Scholes model (Journal of Political Economy 81:637–659, 1973) in which the stock price, follows a log normal process. However, in order to reach a closed form solution for the American option price with one known dividend, Roll (Journal of Financial Economics 5:251–258, 1977), Geske (Journal of Financial Economics 7: 63–81, 1979), and Whaley (Journal of Financial Economics 9:207–211, 1981) assume a displaced lognormal process for the cum-dividend stock price which results in a lognormal process for the ex-dividend stock price. We compare the two alternative pricing results in this paper.

The purpose of this paper is to develop certain relatively recent mathematical discoveries known generally as

stochastic calculus

, or more specifically as

Itô’s Calculus

and to also illustrate their application in the pricing of options. The mathematical methods of stochastic calculus are illustrated in alternative derivations of the celebrated Black–Scholes–Merton model. The topic is motivated by a desire to provide an

intuitive

understanding of certain probabilistic methods that have found significant use in financial economics.

In this paper we review the renowned Constant Elasticity of Variance (CEV) option pricing model and give the detailed derivations.There are two purposes of this article. First, we show the details of the formulae needed in deriving the option pricing and bridge the gaps in deriving the necessary formulae for the model. Second, we use a result by Feller to obtain the transition probability density function of the stock price at time

T

given its price at time

t

with

t

<

T

. In addition, some computational considerations are given which will facilitate the computation of the CEV option pricing formula.

In this chapter, we assume that the volatility of option price model is stochastic instead of deterministic. We apply such assumption to the nonclosed-form solution developed by Scott (Journal of Finance and Quantitative Analysis 22(4):419–438, 1987) and the closed-form solution of Heston (The Review of Financial Studies 6(2):327–343, 1993). In both cases, we consider a model in which the variance of stock price returns varies according to an independent diffusion process. For the closed form option pricing model, the results are expressed in terms of the characteristic function.

In this chapter, we introduce the definitions of Greek letters. We also provide the derivations of Greek letters for call and put options on both dividends-paying stock and non-dividends stock. Then we discuss some applications of Greek letters. Finally, we show the relationship between Greek letters, with one of the examples from the Black– Scholes partial differential equation.

This paper extends the generalized Cox-Ross- Rubinstein (hereafter GCRR) model of Chung and Shih (

2007

). We provide a further analysis of the convergence rates and patterns based on various GCRR models. The numerical results indicate that the GCRR-XPC model and the GCRR-JR

$$(p = 1/2)$$

model (defined in Table

34.1

) outperform the other GCRR models for pricing European calls and American puts. Our results confirm that the node positioning and the selection of the tree structures (mainly the asymptotic behavior of the risk-neutral probability) are important factors for determining the convergence rates and patterns of the binomial models.

This paper examines a variety of methods for extracting implied probability distributions from option prices and the underlying. The paper first explores nonparametric procedures for reconstructing densities directly from options market data. I then consider local volatility functions, both through implied volatility trees and volatility interpolation. I then turn to alternative specifications of the stochastic process for the underlying. I estimate a mixture of log normals model, apply it to exchange rate data, and illustrate how to conduct forecast comparisons. I finally turn to the estimation of jump risk by extracting bipower variation.

It has been well documented that using the Black-Scholes model to price options with different strikes generates the so-called volatility smile. Many previous papers have attributed the smile to the normality assumption in the Black-Scholes model. Hence, they generalize the Black-Scholes model to incorporate a richer distribution. In contrast to previous studies, our model allows for not only a richer distribution, but also the relaxation of another crucial assumption in the Black-Scholes – continuous trading. We show, using S&P 500 call options, how relaxation of continuous trading explains a non-trivial change in the volatility. When an empirical distribution is considered, the smile is almost completely removed. Market prices of options that differ only in their strike prices are inconsistent with a single volatility for the underlying asset, and this well-known feature is called the volatility smile or smirk. The volatility smile is often attributed to either the non-normality of stock returns or to the impossibility of performing costless arbitrage (rebalancing) in continuous time. In this paper, we consider option pricing models that incorporate no rebalancing and/or a nonparametrically estimated density. We attempt to empirically identify which of these two factors contributes more to the smile bias. Using S&P 500 index options, we find that the model with no rebalancing but with normality has a somewhat diminished smile, and the model with a nonparametric density, but with continuous trading, has a slight smile. Only the model with both a nonparametric density and no rebalancing has no perceptible smile bias.

Recent studies have extended the Black–Scholes model to incorporate either stochastic interest rates or stochastic volatility. But, there is not yet any comprehensive empirical study demonstrating whether and by how much each generalized feature will improve option pricing and hedging performance. This paper fills this gap by first developing an implementable option model in closed-form that admits both stochastic volatility and stochastic interest rates and that is parsimonious in the number of parameters. The model includes many known ones as special cases. Based on the model, both delta-neutral and single-instrument minimum-variance hedging strategies are derived analytically. Using S&P 500 option prices, we then compare the pricing and hedging performance of this model with that of three existing ones that respectively allow for (i) constant volatility and constant interest rates (the Black–Scholes), (ii) constant volatility but stochastic interest rates, and (iii) stochastic volatility but constant interest rates. Overall, incorporating stochastic volatility and stochastic interest rates produces the best performance in pricing and hedging, with the remaining pricing and hedging errors no longer systematically related to contract features. The second performer in the horse-race is the stochastic volatility model, followed by the stochastic interest rates model and then by the Black–Scholes.

In this chapter we introduce the application of the characteristic function in financial research. We consider the technique of the characteristic function useful for many option pricing models. Two option pricing models are derived in details based on the characteristic functions.

The payoffs on the expiration dates of Asian options depend on the underlying asset’s average price over some prespecified period rather than on its price at expiration. In this chapter we outline the possible applications of these options and describe the different methodologies and techniques that exist for their evaluation as well as their advantages and disadvantages.

We have developed a modified Edgeworth binomial model with higher moment consideration for pricing European or American Asian options. If the number of the time steps increases, our numerical algorithm is as precise as that of Chalasani et al. (

1999

), with lognormal underlying distribution for benchmark comparison. If the underlying distribution displays negative skewness and leptokurtosis, as often observed for stock index returns, our estimates are better and very similar to the benchmarks in Hull and White (

1993

). The results show that our modified Edgeworth binomial model can value European and American Asian options with greater accuracy and speed given higher moments in their underlying distribution.

A simple formula is developed for the valuation of uncertain income streams consistent with rational investor behavior and equilibrium in financial markets. Applying this formula to the pricing of an option as a function of its associated stock, the Black–Scholes formula is derived even though investors can trade only at discrete points in time.

This paper will first demonstrate how Microsoft Excel can be used to create the Decision Trees for the Binomial Option Pricing Model. At the same time, this paper will discuss the Binomial Option Pricing Model in a less mathematical fashion. All the mathematical calculations will be done by the Microsoft Excel program that is presented in this paper. Finally, this paper uses the Decision Tree approach to demonstrate the relationship between the Binomial Option Pricing Model and the Black-Scholes Option Pricing Model.

This study uses a novel combinatorial method, the Logical Analysis of Data (LAD), to reverse-engineer and construct credit risk ratings, which represent the creditworthiness of financial institutions and countries. The proposed approaches are shown to generate transparent, consistent, self-contained, and predictive credit risk rating models, closely approximating the risk ratings provided by some of the major rating agencies. The scope of applicability of the proposed method extends beyond the rating problems discussed in this study, and can be used in many other contexts where ratings are relevant. The proposed methodology is applicable in the general case of inferring an objective rating system from archival data, given that the rated objects are characterized by vectors of attributes taking numerical or ordinal values.

In this article we present a survey of recent developments in the structural approach to modeling of credit risk. We first review some models for measuring credit risk based on the structural approach. We then discuss the empirical evidence in the literature on the performance of structural models of credit risk.

We develop a comprehensive empirical specification that treats risk-management and risk-taking as integrated facets of a financial intermediary’s risk profile. Three main results emerge from a sample of 518 U.S. bank holding companies during 1991–2000: (1) The corporate risk-management theories most consistently supported are those related to financial distress costs and debt holder-related agency costs (with weaker support for the rationales related to managerial contracting costs, firm size, and hedge substitutes); (2) the asymmetric information theory for managing risk is not supported by our sample; (3) a conventional linear model of risk-management adequately explains cross-sectional and time-series variation in the sample. The model’s findings are robust to alternate definitions of the independent variables, major changes in bank regulation, firm-specific fixed effects, nonlinearities and interactions between the independent variables, as well as firm-specific controls for other key risks related to credit quality and operating efficiency.

Almost every financial institution devotes a lot of attention and energy to credit risk. The default correlations of credit assets have a fatal influence on credit risk. How to model default correlation correctly has become a prerequisite for the effective management of credit risk. In this thesis, we provide a new approach to estimating future credit risk on target portfolio based on the framework of CreditMetrics

TM

by J.P. Morgan. However, we adopt the perspective of factor copula and then bring the principal component analysis concept into factor structure to construct a more appropriate dependence structure among credits. In order to examine the proposed method, we use real market data instead of virtual ones. We also develop a tool for risk analysis that is convenient to use, especially for banking loan businesses. The results indicate that people assume dependence structures are normally distributed, which could lead to underestimated risks. On the other hand, our proposed method captures better features of risks, including conspicuous fat-tail effects, even though the factors appear normally distributed.

This paper first reviews the recent literature on the Unspanned Stochastic Volatilities (USV) documented in the interest rate derivatives markets. The USV refers to the volatilities factors implied in the interest rate derivatives prices that have little correlation with the yield curve factors. We then present the result in Li and Zhao (J Finance 61:341–378, 2006) that a sophicated DTSM without USV feature can have serious difficulties in hedging caps and cap straddles, even though they capture bond yields well. Furthermore, at-the-money straddle hedging errors are highly correlated with cap-implied volatilities and can explain a large fraction of hedging errors of all caps and straddles across moneyness and maturities. These findings strongly suggest that the unmodified dynamic term structure models, assuming the same set of state variables for both bonds and derivatives, are seriously challenged in capturing the term structure volatilities. We also present a multifactor term structure model with stochastic volatility and jumps that yields a closed-form formula for cap prices from Jarrow et al. (J Finance 62:345–382, 2007). The three-factor stochastic volatility model with Poisson jumps can price interest rate caps well across moneyness and maturity. Last we present the nonparametric estimation results from Li and Zhao (Rev Financ Stud, 22(11):4335–4376, 2009). Specifically, the forward densities depend significantly on the slope and volatility of LIBOR rates, and mortgage markets activities have strong impacts on the shape of the forward densities. These results provide nonparametric evidence of unspanned stochastic volatility and suggest that the unspanned factors could be partly driven by activities in the mortgage markets. These findings reinforce the claim that term structure models need to accommodate the unspanned stochastic volatilities in pricing and hedging interest rate derivatives.

This study reviews the valuation models for three types of catastrophe-linked instruments: catastrophe bonds, catastrophe equity puts, and catastrophe futures and options. First, it looks into the pricing of catastrophe bonds under stochastic interest rates and examines how (re)insurers can apply catastrophe bonds to reduce the default risk. Second, it models and values the catastrophe equity puts that give the (re)insurer the right to sell its stocks at a predetermined price if catastrophe losses surpass a trigger level. Third, this study models and prices catastrophe futures and catastrophe options contracts that are based on a catastrophe index.

This study applies a modification of the Schwartz and Moon (Financial Analysts Journal 56:62–75, 2000) model to the evaluation of bank consolidation. From our examination of a bank merger case study (the first example of such a bank merger in Taiwan), we find that, from an ex-ante viewpoint, the consolidation value is, on average, about 30% of the original total value of the independent banks. We also find that the probability of bankruptcy was considerably lower following the merger than it would have been prior to the merger. Our case study therefore indicates that the merger was indeed a worthwhile venture for both banks involved. Furthermore, on completion of the merger, we are also able to determine that, in terms of the magnitude of the increased consolidation value, the most crucial roles are played by the resultant changes in the growth rates of the integrated loans and integrated deposits, as well as the cost-saving factors within the cost functions.

The meltdown of the US subprime mortgage market in 2007 triggered a series of global credit events. Major financial institutions have written down approximately $120 billion of their assets to date and yet there does not seem to be an end to this credit crunch. With traditional mortgage research methods for estimating subprime losses clearly not working, revised modeling techniques and a fresh look at other macroeconomic variables are needed to help explain the crisis. During the subprime market rise/fall era, the levels of the house price index (HPI) and its annual house price appreciation (HPA) had been deemed the main blessing/curse by researchers. Unlike traditional models, our Dynamic Econometric Loss (DEL) model applies not only static loan and borrower variables, such as loan term, combined-loan-to-value ratio (CLTV), and Fair Isaac Credit Score (FICO), as well as dynamic macroeconomic variables such as HPA to project defaults and prepayments, but also includes the spectrum of delinquencies as an error correction term to add an additional 15% accuracy to our model projections. In addition to our delinquency attribute finding, we determine that cumulative HPA and the change of HPA contribute various dimensions that greatly influence defaults. Another interesting finding is a significant long-term correlation between HPI and disposable income level (DPI). Since DPI is more stable and easier to model for future projections, it suggests that HPI will eventually adjust to coincide with the DPI growth rate trend and that HPI could potentially experience as much as an additional 14% decline by the end of 2009.

This research sets out to investigate the relationship between credit risk and equity liquidity. We posit that as the firm’s default risk increases, informed trading increases in the firm’s stock and uninformed traders exit the market. Market-makers widen spreads in response to the increased probability of trades against informed investors. Using the default likelihood measure calculated by Merton’s method, this paper investigates whether financially ailing firms do indeed have higher bid-ask spreads. The panel threshold regression model is employed to examine the possible non-linear relationship between credit risk and equity liquidity. Since high default probability and worse economic prospects lead to greater expropriation by managers, and thus greater asymmetric information costs, liquidity providers will incur relatively higher costs and will therefore offer higher bid-ask spreads. This issue is further analyzed by investigating whether there is any evidence of increased vulnerability in the equity liquidity of firms with high credit risk. Our results show that the effects caused by increased default likelihood might precipitate investors’ loss of confidence in equities trading and thus a decrease in liquidity as evident during the Enron crisis period.

In this paper, we briefly review the pricing of deposit insurance under the option approach. First, we review the theoretical works of deposit insurance pricing model. And second, we summarize the applications of deposit insurance pricing model, focusing on the issue of whether fees charged by the insuring agency are excessive.

Using quantile regression, our results provide explanations for the inconsistent findings that use conventional OLS regression in the extant literature. While the direct effects of R&D investments, leverage, and main bank relationship on Tobin’s Q are insignificant in OLS regression, these effects do show significance in quantile regression. We find that firms’ advantages with high R&D investment over low R&D monotonically increase with firm value, appearing only for high Q firms; while firms’ advantages with low R&D over high R&D monotonically increase with firm value for low Q firms. Tobin’s Q is monotonically increasing with leverage for low Q firms; whereas it is decreasing in high Q firms. Main banks add value for low to median Q firms, while value is destroyed for high Q firms. Meanwhile, we find the interacted effect of main bank and R&D investment which increases with firm value, only appears in medium quantiles, instead of low or high quantiles. Results of this work provide relevant implications for policy makers. Finally, we document that industry quantile effect is larger than the industry effect itself, given that most of the firms in higher quantiles gain from industry effects while lower quantile firms suffer negative effects. We also find the results of OLS are seriously influenced by outliers. In stark contrast, quantile regression results are impervious to either inclusion or exclusion outliers.

In this paper we investigate whether laddering is feasible as an equilibrium phenomenon. In initial public offerings (IPOs), laddering is described as the commitment to and the actual purchase of shares in the aftermarket in addition to what the purchasers would have purchased in the absence of laddering, where the motivation to purchase such additional shares is a pre-agreement (tie-in agreement) with the lead underwriter. Under such tie in agreements, the underwriter allocates more shares to the counter parties of the agreement (ladderers) in return for the commitment to purchase additional, possibly pre-specified, quantities of shares (in excess of what they otherwise would have purchased) so as to boost the price of the stock in after-market trading of the IPO. Our model features three distinct sets of traders: insiders who ladder, rational traders who are generally suspicious of price manipulation and willing to invest effort and resources to acquire information about fundamental values, and, finally, momentum traders whose beliefs are conditioned on past prices. We show that laddering is not a sustainable activity unless (1) Underwriters act as a cartel; (2) there is a ready supply of momentum traders and (3) a lack of short-sellers or other skeptics in the aftermarket. If there are traders that behave in a way consistent with rational expectations and remove price inflation, laddering cannot be a profitable strategy.

This paper investigates stock returns presenting fat tails, peakedness (leptokurtosis), skewness, clustered conditional variance, and leverage effects. We apply the exponential generalized beta distribution of the second kind (EGB2) to model stock returns as measured by six AMEX industry indices. The evidence suggests that the error assumption based on the EGB2 distribution is capable of accounting for skewness and kurtosis and therefore of making good predictions about extreme values. The goodness-of-fit statistic provides supporting evidence in favor of an EGB2 distribution in modeling stock returns.

We examine the association between CEO entrenchment and capital structure decisions of Asian firms. We find that firms with higher CEO entrenchment have a lower level of leverage. Specifically, firms with CEOs who chair the board, have a higher CEO tenure, and have a lower proportion of outside directors, have lower leverage. The negative association between CEO entrenchment and corporate leverage is more pronounced in firms with higher agency costs of free cash flow. In addition, for firms with entrenched CEOs, those firms with greater institutional investor equity ownership have higher leverage. This result suggests that active monitoring by large shareholders mitigate sentrenched CEOs’ incentives to avoid debt.

Under martingale and joint-normality assumptions, various optimal hedge ratios are identical to the minimum variance hedge ratio. As empirical studies usually reject the joint-normality assumption, we propose the generalized hyperbolic distribution as the joint log-return distribution of the spot and futures. Using the parameters in this distribution, we derive several widely used optimal hedge ratios: minimum variance, maximum Sharpe measure, and minimum generalized semivariance. Under mild assumptions on the parameters, we find that these hedge ratios are identical. Regarding the equivalence of these optimal hedge ratios, our analysis suggests that the martingale property plays a much important role than the joint distribution assumption.

We examine volatility of returns for corporate bonds around the days when macroeconomic announcements are made. We find that all corporate investment grade (CIG) bonds earn positive announcement-day excess returns, which increase monotonically with maturity. CIG bond excess returns exhibit strong GARCH effects with highly persistent nonannouncement shocks. Volatility is twice as high on announcement days for CIGs where the announcement effect decreases with maturity. Unlike general (nonannouncement) shocks, announcement-day shocks do not persist and only affect announcement-day conditional variance. Furthermore, the dissipation process for CIGs is different from the one for Treasuries, suggesting that hedging CIGs with Treasuries will not be effective on days immediately after announcement. High yield (HY) bonds behave quite differently around macroeconomic announcements than CIG and Treasuries of corresponding maturity. In addition, we find quite strong evidence of asymmetric volatility for CIG and HY bonds where the asymmetric effect is negative for CIG but positive for HY. These asymmetry results are in contrast to weak asymmetry found for Treasury bonds.

This paper extends the methodology of Milonas and Thomadakis (

1997

) to estimate raw material convenience yields with futures prices during the period 1996 to 2005. We define the business cycle of a seasonal commodity with demand/supply shocks and find that the convenience yields for crude oil and agricultural commodity exhibits seasonal behavior. The convenience yield for crude oil is the highest in the winter, while that for agricultural commodities are the highest in the initial stage of the harvest period. The empirical result show that WTI crude oil is more sensitive to high winter demand and that Brent crude oil is more sensitive to shortages in winter supply. The theory of storage points out that the marginal convenience yield on inventory falls at a decreasing rate as inventory increases which could be verified through those products affected by seasonality, but could not be observed by products affected by demand/supply. Convenience yields are negatively related to interest rates The negative relationship implies that the increase in the carry cost of commodity – namely the interest rate – would cause the yield of holding spot to decline. We also show that convenience yields may explain the price spread between WTI and Brent crude oil as well as the ratio between soybean and corn. Our estimated convenience yields are consistent with Fama and French (

1988

) in that commodity prices are more volatile than futures prices at low inventory level, verifying the Samuelson (

1965

) hypothesis that future prices have fewer variables than spot prices at lower inventory levels.

In this paper, we review the most important and representative capital structure models. The capital structure models incorporate contingent claim valuation theory to quantitatively analyze prevailing determinants of capital structure in corporate finance literature. In capital structure models, the valuation of corporate securities and financial decisions are jointly determined. Most of the capital structure models provide closed-form expressions of corporate debt as well as the endogenously determined bankruptcy level, which are explicitly linked to taxes, firm risk, bankruptcy costs, risk-free interest rate, payout rates, and other important variables. The behavior of how debt values (and therefore yield spreads) and optimal leverage ratios change with these variables can thus be investigated in detail.

We introduce actuarial mathematics and its applications in quantitative finance. First, we introduce the traditional actuarial interest functions and use them to price different types of insurance contracts and annuities. Based on the equivalence principle, risk premiums for different payment schemes are calculated. After premium payments and the promised benefits are determined, actuarial reserves are calculated and set aside to cushion the expected losses. Using the similar method, we use actuarial mathematics to price the risky bond, the credit default swap, and the default digital swap, while the interest structure is not flat and the first passage time is replaced by the time of default instead of the future life time.

This paper suggests a Robust Logit method, which extends the conventional logit model by taking outliers into account, to implement forecast of defaulted firms. We employ five validation tests to assess the in-sample and out-of-sample forecast performances, respectively. With respect to in-sample forecasts, our Robust Logit method is substantially superior to the logit method when employing all validation tools. With respect to the out-of-sample forecasts, the superiority of Robust Logit is less pronounced.

In this chapter, we survey modern term structure models for pricing fixed income securities and their derivatives. We first introduce bond pricing theory within the dynamic term structure model (DTSM) framework. This framework provides a general modeling structure in which most popular term structure models are nested. These include affine, quadratic, regime switching, jump-diffusion, and stochastic volatility models. We then review major studies on default-free bonds, defaultable bonds, interest rate swaps and credit default swaps. We outline the key features of these models and evaluate their empirical performance. Finally, we conclude this chapter by summarizing important findings and suggesting directions for future research.

Classical theories of financial markets assume an infinitely liquid market and that all traders act as price takers. This theory is a good approximation for highly liquid stocks, although even there it does not apply well for large traders or for modeling transaction costs. We extend the classical approach by formulating a new model that takes into account illiquidities. Our approach hypothesizes a stochastic supply curve for a security’s price as a function of trade size. This leads to a new definition of a self-financing trading strategy, additional restrictions on hedging strategies, and some interesting mathematical issues.

We integrate previous work in this area and develop a multiperiod model that simultaneously determines bond refunding, bond issuance, maturity structure, cash holdings, and bank borrowing policies. The focus here is on providing the required debt funds in the most cost efficient fashion. A strength of the model is that it allows for time varying interest costs, transaction costs, issuance costs, and refunding costs to be firm specific. The output of the model lays out the optimal financing decisions for each time interval that minimize the total discounted cost of providing the funds that match the requisite funds. By limiting the surplus funds available, the model minimizes the management incentive to overinvest and thereby reduces the agency costs. The model has economic implications for the firm’s financing decisions its default risk, growth opportunities, riskiness of cash flows, and firm size.

This paper describes a business model in a contingent claim modeling framework. The model defines a “primitive firm” as the underlying risky asset of a firm. The firm’s revenue is generated from a fixed capital asset and the firm incurs both fixed operating costs and variable costs. In this context, the shareholders hold a retention option (paying the fixed operating costs) on the core capital asset with a series of growth options on capital investments. In this framework of two interacting options, we derive the firm value. The paper then provides three applications of the business model. First, the paper determines the optimal capital budgeting decision in the presence of fixed operating costs, and shows how the fixed operating cost should be accounted for in an NPV calculation. Second, the paper determines the equity value, the growth option, the retention option as the building blocks of primitive firm value. Using a sample of firms, the paper illustrates a method that compares the equity values of firms in the same business sector. Third, the paper relates the change in revenue to the change in equity value, showing how the combined operating and financial leverage may affect the firm’s valuation and risks.

We present a continuous-time model of asset valuation in which the generated income follows a stochastic process, and the asset-owner allocates this income between reinvestment and payout. The income generating process is identical to the processes in the multiplicative (e.g., Black-Scholes-Samuelson-Merten) and the additive (e.g., Bachelier-Radner-Shepp) models for two alternative extreme values of the capital marginal productivity parameter. For all other values of this parameter, our process exhibits diminishing marginal productivity of capital. Thus, the model is more appropriate than both the multiplicative and the additive models for modeling the valuation of physical assets. Similar to the additive model, and in contrast to the multiplicative model, our model permits bankruptcy and does not allow unbounded growth of asset values. We demonstrate the existence of, and solve for, the optimal threshold company size level for paying dividends. When company size is above this level income is paid out as dividends, and when it is below this level all income is reinvested in the company. We also find the expected time until bankruptcy.

In this paper, we analyze segmentation of financial markets based on the general segmentation bases. In particular, we identify potentially attractive market segments for financial services using a customer dataset. We develop a multi-group discriminant model to classify the customers into three ordinal classes: prime customers, highly valued customers, and price shoppers based on their income, loan activity, and demographics (age). The multi-group classification of customer segments uses both classical statistical techniques and a mathematical programming formulation. For this study we use the characteristics of a real dataset to simulate multiple datasets of customer characteristics. The results of our experiments show that the mathematical programming model in many case consistently outperforms standard statistical approaches in attaining lower Apparent Error Rates (APER) for 100 replications in both high and low correlation cases.

Stock returns are not highly autocorrelated, but there exists a spurious regression bias in predictive regressions for stock returns similar to the classic studies of Yule (Journal of the Royal Statistical Society 89, 1–64, 1926) and Granger and Newbold (Journal of Econometrics 4, 111–120, 1974). Data mining for predictor variables reinforces spurious regression bias because more highly persistent series are more likely to be selected as predictors. In asset pricing regression models with conditional alphas and betas, the biases occur only in the estimates of conditional alphas. However, when time-varying alphas are suppressed and only time-varying betas are considered, the betas become biased. The analysis shows that the significance of many standard predictors of stock returns and time-varying alphas in the literature is often overstated.

This article discusses the issue related to the errors-in-variables (EIV) problem in the asset pricing tests of the Fama-MacBeth two-pass methodology. The two-pass methodology suffers from the well-known errors-in-variables bias that could attenuate the apparent significance of the market beta. This paper provides a new correction for the EIV problem. After the correction, the market beta shows an economically and statistically significant explanatory power for average stock returns, and firm size has much less support than previously known. This article also examines the sensitivity of the EIV correction to the factors involved in the estimation of the market betas.

In this paper we propose to use Monte Carlo Markov Chain methods to estimate the parameters of Stochastic Volatility Models with several factors varying at different time scales. The originality of our approach, in contrast with classical factor models is the identification of two factors driving univariate series at well-separated time scales. This is tested with simulated data as well as foreign exchange data.

Since the seminal paper of Duffie and Kan (

1996

), most empirical research on the term structure of interest rates has focused on a class of linear models, generally referred to as “affine term structure models.” Since these models produce such a closed-form solution for the entire yield curve, they become very tractable in empirical applications. Nonlinearity can be introduced into dynamic models of the term structure of interest rates either by generalizing the affine specification to a quadratic form or by including a Poisson jump component as an additional state variable. In our paper, we survey some recent studies of dynamic models of the term structure of interest rates that incorporate Markov regimes shifts. We not only summarize an early literature of regime-switching models that mainly focus on the short-term interest rate, but also the recent studies considering regime-switching models in discrete-time and continuous-time, respectively.

The class of

ARM (Autoregressive Modular)

processes is a class of stochastic processes, defined by a nonlinear autoregressive scheme with modulo-1 reduction and additional transformations. ARM processes constitute a versatile class designed to produce high-fidelity models from stationary empirical time series by fitting a strong statistical signature consisting of the empirical marginal distribution (histogram) and the empirical autocorrelation function. More specifically, fitted ARM processes guarantee the matching of arbitrary empirical distributions, and simultaneously permit the approximation of the leading empirical autocorrelations. Additionally, simulated sample paths of ARM models often resemble the data to which they were fitted. Thus, ARM processes aim to provide both a quantitative and qualitative fit to empirical data. Fitted ARM models can be used in two ways: (1) to generate realistic-looking Monte Carlo sample paths (e.g., financial scenarios), and (2) to forecast via point estimates as well as confidence intervals. This chapter starts with a high-level discussion of stochastic model fitting and explains the fitting approach that motivates the introduction of ARM processes. It then continues with a review of ARM processes and their fundamental properties, including their construction, transition structure, and autocorrelation structure. Next, the chapter proceeds to outline the ARM modeling methodology by describing the key steps in fitting an ARM model to empirical data. It then describes in some detail the ARM forecasting methodology, and the computation of the conditional expectations that serve as point estimates (forecasts of future values) and their underlying conditional distributions from which confidence intervals are constructed for the point estimates. Finally, the chapter concludes with an illustration of the efficacy of the ARM modeling and forecasting methodologies through an example utilizing a sample from the S&P 500 Index.

Extant research offers mixed empirical results on the information content of private placements. Hertzel and Smith (J Finance 48:459–485, 1993) suggest that, on average, private placement firms are undervalued. On the other hand, Hertzel et al. (J Finance 57:2595–2617, 2002) show that private placement firms experience significant negative long-run postannouncement stock price performance and that high levels of capital expenditures around private placement reflect managerial overoptimism. Empirical work examining the information content of private placements typically takes the approach based on proxies for information asymmetry that suffers the intrinsic errors-in-variables problem. This paper circumvents the empirical difficulty by developing the two-stage estimation approach and the conditional correlation approach. The conditional correlation coefficient varies between − 1 and + 1 that allows comparisons across samples feasible. Thus, it prevails over the two-stage estimation approach to identify the significance of the information content of equity-selling mechanisms.

In Heston’s stochastic volatility framework, the main problem when implementing Heston’s semi-analytic formula for European-style financial claims is the inverse Fourier integration. The numerical integration scheme of a logarithm function with complex arguments has puzzled practitioners for many years. Without good implementation procedures, the numerical results obtained from Heston’s formula may not be robust, even for customarily used Heston parameters, as the time to maturity is increased. In this chapter, we compare three major approaches to solving the numerical instability problem inherent in the fundamental solution of the Heston model.

This paper tests for the generalized autoregressive conditional heteroscedasticity (GARCH) effect on U.S. stock markets for different periods and reexamines the findings in Lamoureux and Lastrapes (Journal of Finance 45(1):221–229, 1990) by using alternative proxies for information flow, which are included in the conditional variance equation of a GARCH model. We also examine the spillover effects of volume and turnover on the conditional volatility using a bivariate GARCH approach. Our findings show that volume and turnover have effects on conditional volatility and that the introduction of volume/turnover as exogenous variable(s) in the conditional variance equation reduces the persistence of GARCH effects as measured by the sum of the GARCH parameters. Our results confirm the existence of the volume effect on volatility, consistent with the findings by Lamoureux and Lastrapes (Journal of Finance 45(1):221–229, 1990) and others, suggesting that the earlier findings were not a statistical fluke. Our findings also suggest that, unlike other anomalies, the volume effect on volatility is not likely to be eliminated after discovery. In addition, our study rejects the pure random walk hypothesis for stock returns. Our bivariate analysis also indicates that there are no volume or turnover spillover effects on conditional volatility among the companies, suggesting that the volatility of a company’s stock return may not necessarily be influenced by the volume and turnover of other companies.

The impact of implicit “Fuzziness” is inevitable due to the subjective assessment made by investors. Human judgment of events may be significantly different based on individuals’ subjective perceptions or personality tendencies for judgment, evaluation and decisions; thus human judgment is often fuzzy. So we will use the fuzzy set theory to describe and eliminate the “fuzziness” that is the subjective assessment made by investors. Due to the fluctuation of the financial market from time to time, in reality, the future state of a system might not be known completely due to lack of information, so investment problems are often uncertain or vague in a number of ways. The traditional probability financial model does not take into consideration the fact that investors often face fuzzy factors. Therefore, the fuzzy set theory may be a useful tool for modeling this kind of imprecise problem. This theory permits the gradual assessment of the membership of elements in relation to a set; this is described with the aid of a membership function valued in the real unit interval (0, 1). The fuzzy set theory allows the representation of uncertainty and inexact information in the form of linguistic variables that have been applied to many areas. The application of the fuzzy set theory to finance research is proposed in this article.

This short primer provides an overview of the nature and variety of hedonic pricing models that are employed in the market for real estate. It explores the history of hedonic modeling and summarizes the field’s utility-theory-based, microeconomic foundations. It also provides empirical examples of each of the three principal methodologies and a discussion of and potential solutions for common problems associated with hedonic modeling.

This paper provides a general survey of important PDE numerical solutions and studies in detail of certain numerical methods specific to finance with programming samples. These important numerical solutions for financial PDEs include finite difference, finite volume, and finite element. Finite difference is simple to discretize and easy to implement; however, explicit method is not guaranteed stable. The finite volume has an advantage over finite difference in that it does not require a structured mesh. If a structured mesh is used, as in most cases of pricing financial derivatives, the finite volume and finite difference method yield the same discretization equations. Finite difference method can be considered a special case of the finite element method. In general, the finite element method has better quality in obtaining an approximated solution when compared to the finite difference method. Since most PDEs in financial derivatives pricing have simple boundary conditions, the implicit method of finite difference is preferred to finite element method in applications of financial engineering.

The most common capital budgeting approaches use the basic constant risk-adjusted discount models. The most popular valuation approach discounts the unlevered cash flows by the after-tax weighted average cost of capital. The adjusted present value (APV) approach takes the sum of the present value of the unlevered cash flow discounted by the cost of equity of the unlevered firm and the value of the tax benefits of debt discounted by the cost of debt. Traditional approaches for calculating the after-tax weighted average cost of capital and cost of equity of the unlevered firm assume that firms maintain a constant market-value percentage of debt. However, firms typically maintain a book-value percentage of debt. Brick and Weaver (Rev Quant Finance Account 9:111–129, 1997) present an approach to estimate the cost of equity of an unlevered firm when the firm maintains a constant book-value-based leverage ratio. We demonstrate that both the Modigliani and Miller (Am Econ Rev 53:433–443, 1963) and Miles and Ezzell (J Finan Quant Anal 15:719–730, 1980) approaches may yield substantial valuation errors when firms determine debt levels based on book-value percentages. In contrast, our method makes no errors as long as managers know the marginal tax benefit of debt. If the managers do not know the marginal tax benefits of debt, our approach will still result in the smallest valuation error.

The last few decades has witnessed a dramatic growth of U.S.-based mutual funds that invest in non-U.S. stock markets. This paper provides a comprehensive analysis of flows into these international mutual funds for 1970–2003. Our analysis uncovers several new facts about mutual fund flows. First, the empirical findings show a strong relationship between flows into U.S.-based international mutual funds and the correlation between the returns of the fund’s assets and the returns of the U.S. market, consistent with investors’ desire for international diversification. Furthermore, a stronger flow-performance relationship is observed when these correlations are low. As expected, the flows are lower when the volatility of the fund is higher. Second, the flows are related to contemporaneous and past fund returns supporting an “information asymmetry” as well as “return chasing” hypothesis for international capital flows.

This chapter introduces a new method of forecasting,

defensive forecasting

, and illustrates its potential by showing how it can be used to predict the yields of corporate bonds in real time.Defensive forecasting identifies a betting strategy that succeeds if forecasts are inaccurate and then makes forecasts that will defeat this strategy. The theory of defensive forecasting is based on the game-theoretic framework for probability introduced by Shafer and Vovk in 2001. In this framework, we frame statistical tests as betting strategies. We reject a hypothesis when a strategy for betting against it multiplies the capital it risks by a large factor. We prove each classical theorem, such as the law of large numbers, by constructing a betting strategy that multiplies the capital it risks by a large factor if the theorem’s prediction fails. Defensive forecasting plays against strategies of this type.

There has been a rapid growth of range volatility due to the demand of empirical finance. This paper contains a review of the important development of range volatility, including various range estimators and range-based volatility models. In addition, other alternative models developed recently, such as range-based multivariate volatility models and realized ranges, are also considered here. Finally, this paper provides some relevant financial applications for range volatility.

Because of its very important role in modern production and management, information technology (IT) has become a major driver of economic growth and has speeded up the integration of the global economy since the 1990s. Due to the prominent position of the IT industry in the U.S., the U.S. IT stock market is believed to have driven up IT stock markets in other countries. In this paper, we adopt a multivariate GARCH model of Baba et al. (Unpublished manuscript, Department of Economics, University of California, San Diego, 1990) to investigate the linkages between the IT stock and several non-U.S. IT markets; namely, Japan, France, Canada, Finland, Sweden, and Hong Kong. Our findings reveal that, generally, the U.S. IT market contributes strong volatility to non-U.S. IT markets rather than having a mean spillover effect, implying that the U.S. IT market plays a dominant role in the volatility of world IT markets. In addition, our analysis of the dynamic path of correlation coefficients implies that during the formation, spread, and collapse of the IT bubble, the relationships between the U.S. and non-U.S. IT markets are strong but the relationships weaken after the IT bubble bursts.

This chapter introduces ordinary differential equation (ODE) and its applications in finance and economics research. There are various approaches to solve an ordinary differential equation. Among them, the most commonly used approaches are the classical approach for a linear ODE and the Laplace transform approach. We demonstrate the applications of ODE in both deterministic and stochastic systems. As an application in deterministic systems, we apply ODE to solve a simple gross domestic product (GDP) model and an investment model of a firm, which is well studied in Gould (The Review of Economic Studies 1, 47–55, 1968). As an application in stochastic systems, we employ ODE in a jump-diffusion model and derive the expected discounted penalty given the asset value follows a phase-type jump diffusion process. In particular, we study capital structure management model and derive the optimal default-triggering level. For related results, please see Chen et al. (Finance and Stochastics 11, 323–355, 2007).

This chapter introduces the concept of simultaneous equation system and the application of such a system to finance research. We first discuss the order and rank condition of identification problem. We then introduce the two-stage least squares (2SLS) and three-stage least squares (3SLS) estimation method. The pro and cons of these estimations methods are summarized. Finally, the results of a study in executive compensation structure and risk-taking are used to illustrate the difference between single equation and simultaneous equation method.

To reduce the complexity in computing trade-offs among multiple objectives, our series of papers adopts a fuzzy set approach to solve various accounting or finance problems such as international transfer pricing, human resource allocation, accounting information system selection, and capital budgeting problems. A solution procedure is proposed to systematically identify a satisfying selection of possible solutions that can reach the best compromise value for the multiple objectives and multiple constraint levels. The fuzzy solution can help top management make a realistic decision regarding its various resource allocation problems as well as the firm’s overall strategic management when environmental factors are uncertain. In addition, we provide asn update on the effectiveness of a multiple criteria linear programming (MCLP) approach to data mining for bankruptcy prediction using financial data. Data mining applications have been receiving more attention in general business areas, but there is a need to use more of these applications in accounting and finance areas when dealing with large amounts of financial and non-financial data. The results of the MCLP data mining approach in our bankruptcy prediction studies are promising and may extend to other countries.

The information content of implied volatilities and intraday returns is compared in the context of forecasting index volatility over horizons from 1 to 20 days. Forecasts of two measures of realized volatility are obtained after estimating ARCH models using daily index returns, daily observations of the

VIX

index of implied volatility, and sums of squares of 5-min index returns. The in-sample estimates show that nearly all relevant information is provided by the

VIX

index, and hence there is not much incremental information in high-frequency index returns. For out-of-sample forecasting, the

VIX

index provides the most accurate forecasts for all forecast horizons and performance measures considered. The evidence for incremental forecasting information in intraday returns is insignificant.

This paper reviews the literature that deals with structural shifts in statistical models for financial time series. The issue of structural instability is at the heart of capital asset pricing theories on which many modern investment portfolio concepts and strategies rely. The need to better understand the nature of structural evolution and to devise effective control of the risk in real world investments has become ever more urgent in recent years. Since the early 2000s, concepts of financial engineering and the resulting product innovations have advanced in an astonishing pace, but unfortunately often based on a faulty premise, and without proper regulatory keep-ups. The developments have threatened to destabilize worldwide financial markets. We explain the principle and concepts behind these phenomena. Along the way we highlight developments related to these issues over the past few decades in the statistical, econometric, and financial literature. We also discuss recent events that illuminate the dynamics of structural evolution in the mortgage lending and credit industry.

The endogeneity problem has received a mixed treatment in corporate finance research. Although many studies implicitly acknowledge its existence, the literature does not consistently account for endogeneity using formal econometric methods. This chapter reviews the instrumental variables approach to endogeneity from the point of view of a finance researcher who is implementing instrumental variable methods in empirical studies. This review is organized into two parts. Part I discusses the general procedure of the instrumental variables approach, the related diagnostic statistics for assessing the validity of instruments, which are important but not frequently used in finance applications, and some recent advances in econometrics research on weak instruments. Part II surveys corporate finance applications of instrumental variables. We found that the instrumental variables used in finance studies are often chosen arbitrarily and very few diagnostic statistics are performed to assess the adequacy of IV estimation. The resulting IV estimates are thus questionable.

After using the Monty Hall problem to explain Bayes’ rule, we introduce Gibbs sampler and Markov Chain Monte Carlo (MCMC) algorithms. The marginal posterior probability densities obtained by the MCMC algorithms are compared to the exact marginal posterior densities. We present two financial applications of MCMC algorithms: the CKLS model of the Japanese uncollaterized call rate and the Gaussian copula model of S&P500 and FTSE100.

The theoretical literature on the link between an incumbent firm’s capital structure (financial leverage, debt/equity ratio) and entry into its product market is based on two classes of arguments, the “limited liability” arguments and the “deep pocket” arguments. However, these two classes of arguments provide contradictory predictions. This study provides a distinct strategic model of the link between capital structure and entry that is capable of rationally producing both of the existing contradictory predictions. The focus is on the role of beliefs and the cost of adjusting capital structure, two of the factors that are absent in the existing models. The beliefs may be exogenously given or endogenized by a rational expectations criterion.

Vector auto-regression (VAR) models have been used extensively in finance and economic analysis. This paper provides a brief overview of the basic VAR approach by focusing on model estimation and statistical inferences. Applications of VAR models in some finance areas are discussed, including asset pricing, international finance, and market micro-structure. It is shown that such approach provides a powerful tool to study financial market efficiency, stock return predictability, exchange rate dynamics, and information content of stock trades and market quality.

Important results in a large class of financial models of signaling and product market games hinge on assumptions about the second order complementarities or substitutabilities between arguments in the maximand. Such second order relationships are determined by the technology of the firm in signaling models, and market structure in product market games. To the extent that the underlying economics (in theoretical specifications) or the data (in empirical tests) cannot distinguish between such complementarities and substitutabilities, the theoretical robustness and the empirical tests of many models are rendered questionable. Based on three well-known models from finance literature, we discuss the role that these assumptions play in theory development and provide empirical evidence that is consistent with the arguments advanced here.

The phenomenon of long-memory stochastic volatility (LMSV) has been extensively documented for speculative returns. This research investigates the effect of LMSV for estimating the value at risk (VaR) or the quantile of returns. The proposed model allows the return’s volatility component to be short- or long-memory. We derive various types of limit theorems that can be used to construct confidence intervals of VaR for both short-term and long-term returns. For the latter case, the results are in particular of interest to financial institutions with exposure of long-term liabilities, such as pension funds and life insurance companies, which need a quantitative methodology to control market risk over longer horizons.

Dynamic modeling of asset returns and their volatilities is a central topic in quantitative finance. Herein we review basic statistical models and methods for the analysis and forecasting of volatilities. We also survey several recent developments in regime-switching, change-point and multivariate volatility models.

We examine acquirer gains in bids for listed and unlisted targets in a large sample of bank acquisitions. Consistent with findings for the non-financial sector, we report that acquiring firm abnormal returns are significantly larger when the target is unlisted compared to bids for listed targets. Using pre-bid financial data for acquirer and targets in regressions, we estimate the magnitude of the acquisition discount for unlisted firms. We find that the multiple of deal value to target equity is 13.75% lower for unlisted targets, on average, and it is influenced by the method of payment and whether the bid is across state lines.

Under the assumption that the asset value follows a phase-type jump diffusion, we show the expected discounted penalty satisfies an ODE and obtain a general form ?for the expected discounted penalty. In particular, if only downward jumps are allowed, we get an explicit formula in terms of the penalty function and jump distribution. On the other hand, if downward jump distribution is a mixture of exponential distributions (and upward jumps are determined by a general Lévy measure), we obtain closed form solutions for the expected discounted penalty. As an application, we work out an example in Leland’s structural model with jumps. For earlier and related results, see Gerber and Landry [Insurance: Mathematics and Economics 22:263–276, 1998], Hilberink and Rogers [Finance Stoch 6:237–263, 2002], Asmussen et al. [Stoch. Proc. and their App. 109:79–111, 2004] and Kyprianou and Surya [Finance Stoch 11:131–152, 2007].

This paper estimates the cost of equity capital for property/casualty insurers by applying three alternative asset pricing models: the capital asset pricing model (CAPM), the arbitrage pricing theory (APT), and a unified CAPM/APT model (J Finance 43(4), 881–892, 1988). The in-sample forecast ability of the models is evaluated by applying the mean squared error method, the Theil

U

2

(Applied economic forecasting, North-Holland, Amsterdam, 1966) statistic, and the Granger and Newbold (Forecasting economic time series, Academic, New York, 1977) conditional efficiency evaluation. Based on forecast evaluation procedures, the APT and Wei’s unified CAPM/APT models perform better than the CAPM in estimating the cost of equity capital for the PC insurers and a combined forecast may outperform the individual forecasts.

In this paper, we describe the methodology of how to implement a multifactor Cox–Ingersoll–Ross (CIR) models for the term structure of interest rates and its derivatives. We demonstrate how to calibrate the model to the U.S. Treasuries and options on Treasury bond futures.

We present a dynamic term structure model in which interest rates of all maturities are bounded from below at zero. Positivity and continuity, combined with no arbitrage, result in only one functional form for the term structure with three sources of risk. We cast the model into a state-space form and extract the three sources of systematic risk from both the US Treasury yields and the US dollar swap rates. We analyze the different dynamic behaviors of the two markets during credit crises and liquidity squeezes.

Over the past quarter century, mathematical modeling of the behavior of the interest rate and the resulting yield curve has been a topic of considerable interest. In the continuous-time modeling of stock prices, one only need specify the diffusion term, because the assumption of risk-neutrality for pricing identifies the expected change. But this is not true for yield curve modeling. This paper explores what types of diffusion and drift terms forbid negative yields, but nevertheless allow any yield to be arbitrarily close to zero. We show that several models have these characteristics; however, they may also have other odd properties. In particular, the square root model of Cox–Ingersoll–Ross has such a solution, but only in a singular case. In other cases, bubbles will occur in bond prices leading to unusually behaved solutions. Other models, such as the CIR three-halves power model, are free of such oddities.

This paper proposes a generalized functional form CAPM model for international closed-end country funds performance evaluation. It examines the effect of heterogeneous investment horizons on the portfolio choices in the global market. Empirical evidences suggest that there exist some empirical anomalies that are inconsistent with the traditional CAPM. These inconsistencies arise because the specification of the CAPM ignores the discrepancy between observed and true investment horizons. A comparison between the functional forms for share returns and NAV returns of closed-end country funds suggests that foreign investors may have more heterogeneous investment horizons compared to the U.S. counterparts. Market segmentation and government regulation does have some effect on the market efficiency. No matter which generalized functional model we use, the empirical evidence indicates that, on average, the risk-adjusted performance of international closed-end fund is negative even before the expenses.

An incomplete financial market model is considered, where the dynamics of the assets price is described by an

R

d

-valued continuous semimartingale. We express the density of the minimal entropy martingale measure in terms of the value process of the related optimization problem and show that this value process is determined as the unique solution of a semimartingale backward equation. We consider some extreme cases when this equation admits an explicit solution.

We derive the density process of the minimal entropy martingale measure in the stochastic volatility model proposed by Barndorff-Nielsen and Shephard (Journal of the Royal Statistical Society, Series B 63:167–241, 2001). The density is represented by the logarithm of the value function for an investor with exponential utility and no claim issued, and a Feynman–Kac representation of this function is provided. The dynamics of the processes determining the price and volatility are explicitly given under the minimal entropy martingale measure, and we derive a Black and Scholes equation with integral term for the price dynamics of derivatives. It turns out that the price is the solution of a coupled system of two integro-partial differential equations.

In this paper, we discuss the problems of arbitrage detection, which is known as change point detection in statistics. There are some classical methods for change point detection, such as the cumulative sum (CUSUM) procedure. However, when utilizing CUSUM, we must be sure about the model of the data before detecting. We introduce a new method to detect the change points by using Hilbert–Huang transformation (HHT) to devise a new algorithm. This new method (called the HHT test in this paper) has the advantage in that no model assumptions are required. Moreover, in some cases, the HHT test performs better than the CUSUM test, and has better simulation results. In the end, an empirical study of the volatility change based on the S&P 500 is also given for illustration.

This article introduces definitions of the terms bankruptcy, corporate failure, insolvency, as well as the methods of bankruptcy, and popular economic failure prediction models. We will show that a firm filing for corporate insolvency does not necessarily fail to pay off its financial obligations as they mature. Moreover, we will assume an appropriate risk monitoring system centered by well-developed failure prediction models, which is crucial to various parties in the investment world as a means to look after the financial future of their clients or themselves.

This chapter describes the Genetic Programming methodology and illustrates its application for the pricing of options. I describe the various critical elements of a Genetic Program – population size, the complexity of individual formulas in a population, and the fitness and selection criterion. As an example, I implement the Genetic Programming methodology for developing an option pricing model. Using Monte Carlo simulations, I generate a data set of stock prices that follow a Geometric Brownian motion and use the Black–Scholes model to price options off the simulated prices. The Black–Scholes model is a known solution and serves as the benchmark for measuring the accuracy of the Genetic Program. The Genetic Program developed for pricing options well captures the relationship between option prices, the terms of the option contract, and properties of the underlying stock price.

One of the important issues in option pricing is to find a stock return distribution that allows the stock rate of return and its volatility to depend on each other. Cox’s (Notes on option pricing I: constant elasticity of diffusions, unpublished draft, Stanford University, 1975) Constant Elasticity of Variance (CEV) diffusion generates a family of distributions for such a purpose. The main goal of this paper is to review and show the procedures of how such process and its resulting option pricing formula are derived. First, we show how the density function of the CEV diffusion is identified and we demonstrate the option formula by using the Cox and Ross (Journal of Financial Economics 145–166, 1976) methodology. Then, we transform the solution into a non-central chi-square distribution. Finally, a number of approximation formulas are provided.