Advances in Risk Management

Frontmatter

Chapter 1. Impact of the Collection Threshold on the Determination of the Capital Charge for Operational Risk

Abstract

In 2004, the Basel Committee on Banking Supervision (hereafter the Basel Committee) released the Revised Framework of the International Convergence of Capital Measurement and Capital Standards (hereafter Basel II). Together with new rules governing the calculation of regulatory capital charge for credit risk, Basel II introduces explicit recommendations with regard to operational risk, defined by the Basel Committee as the “risk of loss resulting from inadequate or failed internal processes, people and systems or from external events. This definition includes legal risk, but excludes strategic and reputational risk” (BCBS, 2004).

Yves Crama, Georges Hübner, Jean-Philippe Peters

Chapter 2. Incorporating Diversification into Risk Management

Abstract

Risk measurement is of fundamental importance to financial practice. Given the widespread usage of Value-at-Risk (VaR), firms actively manage their risk. Unfortunately, VaR is not derived from fundamental economic principles and may lead to sub-optimal decisions as shown by Shapiro and Basak (2001).

Amiyatosh Purnanandam, Mitch Warachka, Yonggan Zhao, William T. Ziemba

Chapter 3. Sensitivity Analysis of Portfolio Volatility: Importance of Weights, Sectors and Impact of Trading Strategies

Abstract

This chapter discusses the application of a new method to the Sensitivity Analysis (SA) of portfolio properties and proposes an SA scheme that is capable of assessing the joint impact of changes in portfolio composition on portfolio volatility (σ _p ).

Emanuele Borgonovo, Marco Percoco

Chapter 4. Managing Interest Rate Risk under Non-Parallel Changes: An Application of a Two-Factor Model

Abstract

Two decades ago, fixed-income markets experienced a great increase in the volatility of assets dealt in those markets.¹ Because of this academics and market participants developed and implemented tools and techniques to manage the interest rate risk. In particular, we will consider default-free securities and liquid markets. We will distinguish two types of risk: market risk and the yield curve one, associated to parallel and non-parallel changes in the yield curve, respectively.

Manuel Moreno

Chapter 5. An Essay on Stochastic Volatility and the Yield Curve

Abstract

In this chapter we consider the issue of forecasting the stochastic volatility and the yield curve. These two concepts are very important in financial engineering, especially in risk management. Forecasting stochastic volatility is indeed an essential ingredient in VaR computations, and for immunizing bond portfolios a prediction of the yield curve is a sine qua non.

Raymond Théoret, Pierre Rostan, Abdeljalil El-Moussadek

Chapter 6. Idiosyncratic Risk, Systematic Risk and Stochastic Volatility: An Implementation of Merton’s Credit Risk Valuation

Abstract

Originally Sharpe (1963) stated the dependence of stock returns vis-à-vis systematic (for example, market or undiversifiable) risk and idiosyncratic (for example, specific or diversifiable) risk. Indeed, systematic risk is common to any risky asset in the financial market whereas idiosyncratic risk is peculiar to the asset under consideration. Therefore, credit risky assets, such as corporate bonds or debt, should satisfy such a dependence feature. Many authors have investigated this assumption to test whether credit risk is of systematic or idiosyncratic nature. We focus on the most recent findings (see Gatfaoui, 2003, for a brief survey).

Hayette Gatfaoui

Chapter 7. A Comparative Analysis of Dependence Levels in Intensity-Based and Merton-Style Credit Risk Models

Abstract

In finance, especially for credit portfolio modeling, basket credit derivatives (CDOs, n-th to default) pricing and hedging, the building of an accurate measure of the dependence between the underlying default events is becoming a key-challenge (see Crouhy, Galai and Mark, 2002; Koyluoglu and Hickman, 1998, for a review of the current credit risk portfolio models). This new frontier has induced a huge amount of literature for several years: Nyfeler (2000), Frey and McNeil (2001), Schönbucher and Schubert (2001), Das, Geng and Kapadia (2002), Elizalde (2003), Turnbull (2003), Yu (2003), among others.

Jean-David Fermanian, Mohammed Sbai

Chapter 8. The Modeling of Weather Derivative Portfolio Risk

Abstract

The companies that trade weather derivatives typically hold portfolios of between 100 and 1,000 weather derivative contracts. Different contracts have payoffs that may depend on different weather variables measured at different locations over different time periods. The payoffs between any two contracts may be highly correlated or anticorrelated (if they are based on the same or similar variables, locations or time periods), or they may be uncorrelated (if the weather variables, locations or time periods are very different). How, then, should the total financial risk in such portfolios be estimated?

Stephen Jewson

Chapter 9. Optimal Investment with Inflation-Linked Products

Abstract

With the growing number of traded inflation linked bonds and inflation linked life insurance products there is also a growing interest in models for the evolution of inflation indexes and the inclusion of inflation linked financial products into an optimal portfolio of an investor who is otherwise investing in bonds and stocks. We will look at this problem in a model that is a combination of the standard diffusion type model of continuous-time portfolio optimization and a modeling framework for inflation indexes described in Korn and Kruse (2004) (which itself is in some aspects related to Jarrow and Yildirim, 2003).

Taras Beletski, Ralf Korn

Chapter 10. Model Risk and Financial Derivatives

Abstract

Since the introduction of option trading in Chicago in 1973, derivatives have shaped the evolution of capital markets by allowing efficient risk unbundling and transfer. Financial intermediaries immediately recognized that derivatives were the perfect tool to customize state-contingent payoffs for both speculators and hedgers alike. Consequently, the volume and various types of derivative contracts traded on organized exchanges as well as in over the counter markets have grown steadily. The catalysts of this success were the development of financial theory and sophisticated pricing mathematical models, the availability of real-time information, the technological innovation (in particular increasingly powerful computers) as well as the move from open-outcry trading to electronic trading. Today, we have reached the point where derivatives have become an essential feature of practically any financial contract. They have changed the way companies and individuals make investments, raise capital, and even measure, manage and understand risk.

François-Serge Lhabitant

chapter 11. Evaluating Value-at-Risk Estimates: A Cross-Section Approach

Abstract

Since 1998, regulatory guiding principles have required banks with significant trading activity to set aside capital to insure against extreme portfolio losses. The size of the market risk capital requirement is directly related to a measure of portfolio risk. Currently, in the regulatory framework, portfolio risk is measured in terms of its Value-at-Risk (VaR). Also in the community of asset management companies the quest for reliable risk management techniques has grown in recent years. The concept of VaR is now widespread among asset managers. This is an answer to the demand of sophisticated investors, such as pension funds and foundations, and it is also a clear response to the growing interest of asset managers for analytical tools that give better control on their portfolios.

Raffaele Zenti, Massimiliano Pallotta, Claudio Marsala

Chapter 12. Correlation Breakdowns in Asset Management

Abstract

Over recent years, financial and real market globalization has accelerated the process of increasing positive values of correlations. This phenomenon changed many portfolio managers’ practices, which are now strictly linked with sector behaviors. In order to verify whether portfolio managers can correctly estimate the eventual correlation jump over time, we provide some new evidences for correlation dynamics among equity markets.

Riccardo Bramante, Giampaolo Gabbi

Chapter 13. Sequential Procedures for Monitoring Covariances of Asset Returns

Abstract

Time variability of the expected returns as well as the volatility of asset returns can be caused by changes in the fundamental factors; for example, changes in commodity prices, macroeconomic policy, market trading activity, technological development, governmental policies, and so on. This leads to the deviation of a selected optimal portfolio from the Markowitz efficient frontier that consists of all portfolios with the highest expected return for the given level of risk or with the smallest risk for a preselected profit and, thus, is fully defined by the first two moments of asset returns (Markowitz, 1952). Changes in these characteristics are subject to structural breaks of the efficient frontier location in the mean-variance space and the optimal portfolios allocated on it.

Olha Bodnar

Chapter 14. An Empirical Study of Time-Varying Return Correlations and the Efficient Set of Portfolios

Abstract

Modern portfolio theory was first introduced in 1952 (Markowitz, 1952), and since then it has been the mainstay of asset allocation models. In the mean-variance paradigm of Markowitz, an efficient set of portfolios is estimated by maximizing the expected return of the portfolio and minimizing its risk, as measured by the standard deviation. For practical purposes, efficient portfolio construction requires estimation of expected returns and variances of expected returns of individual assets in the portfolio, as well as the covariance matrix of the asset returns. The most widely used method of estimating these inputs into a portfolio model is to use the past return data for a period of five years and use the historic average values of returns, variances and co-variances as proxies for expected values. One of the implicit assumptions in this method of efficient portfolio construction is that the variances and co-variances are time-invariant during the holding period of the portfolio (Jobson and Korkie, 1981).

Thadavillil Jithendranathan

Chapter 15. The Derivation of the NPV Probability Distribution of Risky Investments with Autoregressive Cash Flows

Abstract

Frederick Hillier’s (1963) seminal paper was probably the first to propose the use of probabilistic information to assess risk in the process of capital budgeting. However, such an approach to investment decision was short-lived when Sharpe published his 1964 paper, supplemented by Lintner’s (1965) and Mossin’s (1966) articles, thus setting the conceptual ground for what was to become the modern capital asset pricing model (CAPM). Even Hertz’s (1964) simulation methodology and Wagle’s (1967) statistical analysis of risk in capital investment projects did not fare better. In fact, all the probabilistic approaches to risky investment decisions were swept away by the Sharpe-Lintner-Mossin CAPM revolution as it became the creed of modern financial theory. Such a result was unavoidable given that, under the capital asset pricing theory, the dispersion (as well as the higher moments) in the probability distribution of future cash flows became an irrelevant statistic. Systematic risk, as calculated by the beta, became the only relevant measure of risk.

Jean-Paul Paquin, Annick Lambert, Alain Charbonneau

Chapter 16. Have Volatility Transmission Patterns between the USA and Spain Changed after September 11?

Abstract

On 11 September 2001, the USA experienced its most devastating terrorist attack. This attack had an influence over several economic variables and it obviously affected financial markets. Taking into account the increasing global financial integration, an important question arises: Could recent terrorist attacks have increased even more interrelations between financial markets?

Helena Chuliá, Francisco J. Climent, Pilar Soriano, Hipòlit Torró

Chapter 17. Large and Small Cap Stocks in Europe: Covariance Asymmetry, Volatility Spillovers and Beta Estimates

Abstract

Several studies show that small cap returns tend to behave differently from large cap returns (Banz, 1981; Chan and Chen, 1991). This fact suggests that diversifying into small cap stocks might improve portfolio performance. In fact, the main empirical evidence on small cap returns shows that small caps distinguish themselves from large caps due to economic and market related characteristics (for a literature review on this topic see Petrella, 2005).

Helena Chuliá, Hipòlit Torró

Chapter 18. On Model Selection and its Impact on the Hedging of Financial Derivatives

Abstract

The mathematical theory of derivatives pricing and risk-management is one of the most active fields of research for both academics and practitioners. The celebrated Black-Scholes-Merton (BS) pioneering work paved the way to the development of a general theory of option pricing through the concept of absence of market arbitrage and dynamic replication (Harrison and Pliska, 1981). As is well-known, the simplistic assumptions behind the BS model make it unsuitable to capture and explain the risk borne by complex (exotic) financial derivatives. The need for a departure from the BS paradigm is in fact evident from the analysis of historical time series (Bates, 1996; Pan, 2002; Chernov, Gallant, Ghysels and Tauchen, 2003; and Eraker, Johannes and Polson, 2003, among others), as well as from the observation of the volatility smile phenomenon (Heston, 1993; Dupire, 1994, among others). For these reasons a number of alternative models have been advocated by many authors. Roughly speaking, all dynamic arbitrage-free models aiming at generalizing BS theory can be divided in three main classes, according to the characteristics of the stochastic process driving the dynamics of the underlying assets.

Giuseppe Di Graziano, Stefano Galluccio

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