Fixed-Income Securities Dynamic Methods for Interest Rate Risk Pricing and Hedging

by Martellini, Lionel; Priaulet, Philippe

• ISBN13: 9780471495024
• ISBN10: 0471495026
• Edition: 1st
• Format: Hardcover
• Copyright: 2001-02-08
• Publisher: WILEY

Summary

Dynamic methods for interest rate risk pricing and hedging. Fixed-Income Securities provides a survey of modern methods for pricing and hedging fixed-income securities in the presence of interest rate risk. Modern theory of finance provides a wealth of new approaches to the important question of interest rate risk management, and this book brings them together, in a comprehensive and thorough treatment of the subject. Structured in an accessible manner, the authors begin by focusing on pricing and hedging certain cash flows, before moving on to consider pricing and hedging uncertain cash flows. In addition to the theoretical explanation, the authors provide numerous real-world examples and applications throughout. This is the first book I have seen to carefully cover such a wide set of topics in both theoretical and applied fixed-income modelling, ranging from the use of market information to obtain yield curves, to the pricing and hedging of bonds and fixed-income derivatives, to the currently active topic of defaultable yield-curve modelling. It will be particularly useful to practitioners.Darrell Duffie, Stanford University This is the most comprehensive theoretical treatment of the subject I ve ever seen. Mark Rubinstein, Haas School of Business, University of California An excellent review of interest rate models and of the pricing and hedging principles in the fixed-income area.Oldrich Alfons Vasicek, KMV Corporation

Author Biography

Lionel Martellini is an Assistant Professor of Finance at the Marshall School of Business, University of Southern California. He holds Master’s degrees in Business Administration, Economics, Statistics, and Mathematics, and a PhD in Finance (U.C. Berkeley). He conducts active research in derivatives pricing, credit risk analysis, and quantitative portfolio management and has served as a consultant in these fields for various other financial institutions, in particular ACT Financial Systems. Philippe Priaulet is the Head of Fixed Income Research at Crédit Commercial de France (CCF — Direction of Research and Innovation), member of HSBC group, where he is particularly involved in the bank’s risk management process. His expertise is related to quantitative finance in general and term structure models in particular. He holds a Master’s degree in Business Administration, and a PhD in Financial Economics (Université Paris-IX Dauphine). He also teaches quantitative methods to students in economics and finance at Université Paris-IX Dauphine.

Table of Contents

Introduction	ix
Acknowledgments	xii
Standard Notation	xiii
PART I: PRICING AND HEDGING CERTAIN CASH-FLOWS	1	(88)
Deriving the Current Zero-Coupon Rate Curve	3	(28)
The Direct Method	3	(2)
Indirect Methods	5	(26)
Parameterization of the Discount Function as a Spline Function	6	(12)
Parameterization of the Zero-Coupon Curve as a Function of Different Parameters	18	(9)
Discussion and Comparison of the Methods	27	(1)
Fitting the Zero-Coupon Yield Curve using Data from the Swap Market	28	(3)
Basic Assets Pricing and Hedging	31	(58)
General Principle	41	(8)
Qualification of Interest Rate Risk	41	(1)
Quantification of Interest Rate Risk	42	(7)
Specific Applications	49	(40)
A Simplified Framework: Assuming a Flat Zero-Coupon Yield Curve	49	(12)
More Realistic Frameworks: Accounting for Non-Flat Zero-Coupon Yield Curves	61	(28)
PART II: PRICING AND HEDGING UNCERTAIN CASH-FLOWS	89	(126)
Modelling the Zero-Coupon Yield Curve Dynamics	91	(84)
Equilibrium Models	93	(24)
Single-Factor Models	93	(16)
Multi-Factor Models	109	(8)
Arbitrage Models	117	(49)
General Framework	118	(6)
Markov Models	124	(32)
Market Models: The BGM/Jamshidian Approach	156	(10)
A Classic Example: The Two-Factor `Extended Vasicek' Model	166	(9)
Presentation of the Model	167	(3)
Reconciling the Model with the Results of a PCA on the Yield Curve Variation	170	(2)
Yield Curve Transformations Allowed by the Model	172	(1)
Shortcomings of the Model	173	(2)
Pricing and Hedging Fixed-Income Derivatives	175	(40)
The Black Model: A Market Standard	175	(8)
Pricing and Hedging Caps	176	(4)
Pricing and Hedging Swaptions	180	(3)
Inconsistency in the Market Pricing of Caps and Swaptions	183	(1)
The Two-Factor `Extended Vasicek' Model: Calibration Of The Model	183	(6)
Using a PCA	183	(2)
Using Market Prices	185	(4)
The Two-Factor `Extended Vasicek' Model: Pricing and Hedging	189	(26)
Standard Derivative Pricing	189	(15)
Derivative Hedging	204	(3)
Pricing Defaultable Fixed-Income Claims	207	(8)
PART III: MATHEMATICAL APPENDICES	215	(2)
APPENDIX A: AN INTRODUCTION TO STOCHASTIC PROCESSES IN CONTINUOUS TIME	217	(18)
A.1 Brownian Motion	217	(5)
A.1.1 Standard Brownian Motion	218	(3)
A.1.2 Generalization	221	(1)
A.2 Stochastic Integrals	222	(2)
A.2.1 Construction and Properties	222	(1)
A.2.2 Ito Process	223	(1)
A.3 Stochastic Differential Equations (SDEs)	224	(1)
A.4 Asset Price Process	225	(1)
A.5 Representation Of Brownian Martingales	226	(1)
A.6 Continuous-Time Asset Pricing	226	(7)
A.6.1 Unidimensional Ito's Lemma	226	(3)
A.6.2 A Multidimensional Version of Ito's Lemma	229	(1)
A.6.3 Integration by Parts	230	(1)
A.6.4 Girsanov's Theorem	231	(1)
A.6.5 Application to Finance	232	(1)
A.7 Feynman-Kac Formula	233	(2)
APPENDIX B: NUMERICAL METHODS	235	(8)
B.1 Monte Carlo Simulations	235	(3)
B.1.1 Principle	235	(1)
B.1.2 Generating Asset Paths	236	(1)
B.1.3 Application to Fixed-Income Securities	236	(1)
B.1.4 Generating Multidimensional Processes	237	(1)
B.2 Finite-Difference Methods	238	(5)
B.2.1 General Presentation	238	(1)
B.2.2 Explicit Schemes	239	(1)
B.2.3 Implicit Schemes	240	(3)
References	243	(10)
Index	253