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2018 | Buch

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New Methods in Fixed Income Modeling

Fixed Income Modeling

herausgegeben von: Prof. Mehdi Mili, Dr. Reyes Samaniego Medina, Prof. Filippo di Pietro

Verlag: Springer International Publishing

Buchreihe : Contributions to Management Science

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book presents new approaches to fixed income modeling and portfolio management techniques. Taking into account the latest mathematical and econometric developments in finance, it analyzes the hedging securities and structured instruments that are offered by banks, since recent research in the field of fixed incomes and financial markets has raised awareness for changes in market risk management strategies. The book offers a valuable resource for all researchers and practitioners interested in the theory behind fixed income instruments, and in their applications in financial portfolio management.

Inhaltsverzeichnis

Frontmatter

New Term Structure Modeling Approaches

Frontmatter

Term Structure, Market Expectations of the Short Rate, and Expected Inflation

Abstract

Based on the classic Gaussian dynamic term structure model \( {\mathbb{A}}_{0} \left( 3 \right) \), we rotate the model to a special representation, the so called “Companion Form Realization”, in which the state variables comprise the short rate and its related expectations. This unique feature makes the representation very useful in analyzing the response of the yield curve to the shocks in the short rate and its related expectations, and monitoring market expectations. Using the estimated model, we quantify a variety of yield responses to the changes in these important state variables; and also give an “unsurprising” pattern in which changes in state variables have little impact on the long end of the yield curve. Estimated state variables have strong explanatory power for expected inflation. Three case studies of the unconventional monetary policies are presented.

Jian Luo, Xiaoxia Ye

A New Approach to CIR Short-Term Rates Modelling

Abstract

It is well known that the CIR model, as introduced in 1985, is inadequate for modelling the current market environment with negative short rates, r(t) . Moreover, in the CIR model, the stochastic part goes to zero with the rates, neither volatility nor long term mean change with time, or fit with skewed (fat tails) distribution of r(t) , etc. To overcome the limitations of the CIR, several different approaches have been proposed to date: multi-factor models such as the Hull and White or the Chen models to the CIR++ by Brigo and Mercurio. Here, we explain how our extension of the CIR framework may fit well to market short interest rates.

Giuseppe Orlando, Rosa Maria Mininni, Michele Bufalo

The Heath-Jarrow-Morton Model with Regime Shifts and Jumps Priced

Abstract

The Heath-Jarrow-Morton model is an important tool for describing the term structure of interest rates. A regime switching version was considered by Elliott and Siu (Quant Finance 16(12):1791–1800, 2016). It is of interest to price the risk due to the regime switching and this was discussed in Elliott and Siu (Quant Finance 16(12):1791–1800, 2016). In this paper, an extended Heath-Jarrow-Morton model for stochastic forward rates, incorporating both regime shifts and jumps is considered, where jumps in the forward rate dynamics are directly triggered by the regime switches. No-arbitrage drift conditions, which take into account the pricing of both the regime-switching and jump risks, are derived in two situations. The first situation starts with a risk-neutral measure while the second situation starts with the real-world measure.

Robert J. Elliott, Tak Kuen Siu

Explicit Computation of the Post-crisis Spot LIBOR in a Jump-Diffusion Framework

Abstract

Starting from the worldwide financial crisis originated by the dramatic US economic events happened in 2007, many markets have seen a sudden growth of heterogeneous risk types, spanning from credit ones to liquidity ones. These abrupt changes in fundamentals, have produced the develop of significant spreads between the same interbank rate, e.g. the LIBOR rate, considered at different tenors. In the present chapter, we show how to explicitly compute the post-crisis spot LIBOR at different tenors, taking into account the possibility of jumps in the instantaneous spot rate trajectories, representing, in our setting, the so called OIS short-rate. Such an analysis is based on the intensity approach, where large and sudden movements can be modeled by adding marked point processes to the classical diffusion interest rate framework. Rigorous computations are also provided according with appropriate assumptions on the jumps intensity shape.

Luca Di Persio, Nicola Gugole

An Overview of Post-crisis Term Structure Models

Abstract

This chapter is intended to provide an overview of state-of-the-art term structure models used in pricing and risk managing interest rate dependent financial products as well as forecasting interest rates in economic scenario generators for market and counterparty credit risk management purposes. After introducing a general overview of the post-crisis markets environment we will provide insight into post-crisis modelling of term structures via short rate models and Libor Market models for multiple curves and show how these models are applied in economic scenario generators used for risk management and pricing purposes alike.

Marcus R. W. Martin

A Comparison of Estimation Techniques for the Covariance Matrix in a Fixed-Income Framework

Abstract

We compare various methodologies to estimate the covariance matrix in a fixed-income portfolio. Adopting a statistical approach for the robust estimation of the covariance matrix, we compared the Shrinkage (SH), the Nonlinear Shrinkage (NSH), the Minimum Covariance Determinant (MCD) and the Minimum Regularised Covariance Determinant (MRCD) estimators against the sample covariance matrix, here employed as a benchmark. The comparison was run in an application aimed at individuating the principal components of the US term structure curve. The contribution of the work mainly resides in the fact that we give a freshly new application of the MRCD and the NS robust covariance estimators within the fixed-income framework. Results confirm that, likewise financial portfolios, also fixed-income portfolios can benefit of using robust statistical methodologies for the estimation of the covariance matrix.

Marco Neffelli, Marina Resta

The Term Structure Under Non-linearity Assumptions: New Methods in Time Series

Abstract

In this chapter, we summarized an empirical review of the EHTS aiming to establish the adequate procedures for its measurement by using time series. On one hand, the chapter discusses the main findings in the literature in the USA and the EMU and, on the other hand, analyses the linearity restrictions associated with the traditional approaches used in time series applications on term structure. The use of FCVAR represents a novel procedure to solve the linearity restrictions. Finally, this application allows the economic policies that derive from its results to be more appropriate for the objectives of the design of monetary policies.

José Carlos Vides, Jesús Iglesias, Antonio A. Golpe

Affine Type Analysis for BESQ and CIR Processes with Applications to Mathematical Finance

Abstract

This chapter aims presents the deep relationships between the Cox-Ingersoll-Ross (CIR) type-processes, the Squared Bessel (BESQ) processes and the family of affine processes, according to specific dynamics for the dividend structure behind the market scenarios, aiming at deriving pricing formulas in individual markets as well as analytical solvable or numerical tractable, schemes for dividend processes in volatility stabilized markets.

Luca Di Persio, Luca Prezioso

New Advances in Fixed Income Management

Frontmatter

Sensitivity Analysis and Hedging in Stochastic String Models

Abstract

We analyze certain results on the stochastic string modeling of the term structure of interest rates and we apply them to study the sensitivities and the hedging of options with payoff functions homogeneous of degree one. Under the same framework, we use an exact multi-factor extension of Jamshidian (1989) to find the sensitivities for swaptions and we prove that it cannot be applied to captions. We present a new approximate result for pricing options on coupon bonds based on the Fenton-Wilkinson method and we show that it generalizes the fast coupon bond option pricing proposed in Munk (1999). This result can be easily applied to the approximate valuation of swaptions and captions.

Alberto Bueno-Guerrero, Manuel Moreno, Javier F. Navas

Hedging Asian Bond Options with Malliavin Calculus Under Stochastic String Models

Abstract

In this chapter we use some recent hedging results for bond options, obtained with Malliavin calculus in the context of the stochastic string framework, to hedge different types of Asian options. In all the cases, we show that the hedging portfolio has no bank account part.

Alberto Bueno-Guerrero, Manuel Moreno, Javier F. Navas

Stochastic Recovery Rate: Impact of Pricing Measure’s Choice and Financial Consequences on Single-Name Products

Abstract

The ISDA CDS pricer is the market-standard model to value credit default swaps (CDS). Since the Big Bang protocol moreover, it became a central quotation tool: just like options prices are quoted as implied vols with the help of the Black-Scholes formula, CDSs are quoted as running (conventional) spreads. The ISDA model sets the procedure to convert the latter to an upfront amount that compensates for the fact that the actual premia are now based on a standardized coupon rate. Finally, it naturally offers an easy way to extract a risk-neutral default probability measure from market quotes. However, this model relies on unrealistic assumptions, in particular about the deterministic nature of the recovery rate. In this paper, we compare the default probability curve implied by the ISDA model to that obtained from a simple variant accounting for stochastic recovery rate. We show that the former typically leads to underestimating the reference entity’s credit risk compared to the latter. We illustrate our views by assessing the gap in terms of implied default probabilities as well as on credit value adjustments (CVA) figures and pricing mismatches of financial products like deep in-/out-of-the-money standard CDSs and digital CDSs (main building block of credit linked notes, CLNs).

Paolo Gambetti, Geneviève Gauthier, Frédéric Vrins

Dynamic Linkages Across Country Yield Curves: The Effects of Global and Local Yield Curve Factors on US, UK and German Yields

Abstract

We analyze the relationship between the yield curves of the USA, the UK and Germany using global and local factors. Our focus is on dynamic linkages across and between yield curves and factors. We disentangle the latent global and local factors contained in country factors, based on the Diebold and Li (J Econometrics 130:337–364, 2006) parametrization of Nelson and Siegel’s (1987) three factor model and a quasi-maximum likelihood approach. The results indicate that global factors explain on average 55% of the variance of yields. Using impulse response analysis, we examine the effects of shocks to the factors on yields. We find that the response of yields to shocks to global factors is larger and longer-lasting than the response to shocks to local factors.

Laura Coroneo, Ian Garrett, Javier Sanhueza

Estimating the No-Negative-Equity Guarantee in Reverse Mortgages: International Sensitivity Analysis

Abstract

In this paper, we perform a sensitivity analysis to show how the value of the no-negative-equity guarantee (NNEG) embedded in reverse mortgage contracts varies with the value of the mortgage roll-up rate, the rental yield rate, as well as the gender and the age of the borrower. The analysis is performed for four European countries: France, Germany, Spain and the United Kingdom. The results show that the NNEG tends to be higher, and consequently the reverse mortgage provider faces higher risks, for higher roll-up rates, for higher rental yield rates, for the female population, and for relatively young borrowers. Moreover, the country with the highest estimated value of the NNEG is Spain, the country most affected by the 2008 financial crisis.

Iván de la Fuente, Eliseo Navarro, Gregorio Serna

Institutional Versus Retail Investors’ Behavior Around Credit Rating News

Abstract

This paper investigates the impact of credit rating downgrades on the liquidity and trading behavior of both segments of trading in the U.S. corporate bond market: the institutional- and the retail-sized ones. Using the TRACE dataset, we test if both market segments behave different and what hypotheses explain this potential divergence. We test the regulatory constraints hypothesis (regulatory mandates may force institutional bondholders to sale downgraded bonds), the informed-uninformed traders’ hypothesis (information could be responsible for different trading activity patterns before credit rating changes depending the segment of trading), and the usual information hypothesis. We obtain evidence of increased trading activity and price adjustments around downgrades for both segments. Rating-contingent regulation induces larger intensity responses in the institutional segment. Finally, we observe trading anticipation before downgrades that is consistent with the existence of informed institutional investors.

Pilar Abad, Antonio Díaz, Ana Escribano, M. Dolores Robles

The Market and Individual Pricing Kernels Under No Arbitrage Asset Pricing Models

Abstract

This chapter discusses how to use the No Arbitrage Asset Pricing Model (NAAPM) to determine the pricing kernel for both the financial markets and an individual with a given degree of constant risk aversion over her terminal wealth. The existence of the market and individual pricing kernel allows us to value any financial contract whose payoff is dependent on the prices from the NAAPM. Consequently, an individual would raise her lifetime utility by buying the assets which she prices higher than the financial market.

Thomas F. Cosimano, Jun Ma

Titel: New Methods in Fixed Income Modeling
herausgegeben von: Prof. Mehdi Mili
Dr. Reyes Samaniego Medina
Prof. Filippo di Pietro
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-95285-7
Print ISBN: 978-3-319-95284-0
DOI: https://doi.org/10.1007/978-3-319-95285-7