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by Lixin Wu (Author)
About the Author
Lixin Wu is a professor at the Hong Kong University of Science and Technology. Best known in the financial engineering community for his work on market models, Dr. Wu co-developed the PDE model for soft barrier options and the finite-state Markov model for credit contagion.
About this book
Containing many results that are new, or which exist only in recent research articles, Interest Rate Modeling: Theory and Practice, 2nd Edition portrays the theory of interest rate modeling as a three-dimensional object of finance, mathematics, and computation. It introduces all models with financial-economical justifications, develops options along the martingale approach, and handles option evaluations with precise numerical methods.
Features
- Presents a complete cycle of model construction and applications, showing readers how to build and use models
- Provides a systematic treatment of intriguing industrial issues, such as volatility and correlation adjustments
- Contains exercise sets and a number of examples, with many based on real market data
- Includes comments on cutting-edge research, such as volatility-smile, positive interest-rate models, and convexity adjustment
- New to the 2nd edition: volatility smile modeling; a new paradigm for inflation derivatives modeling; an extended market model for credit derivatives; a dual-curved model for the post-crisis interest-rate derivatives markets; and an elegant framework for the xVA.
Brief contents
1 The Basics of Stochastic Calculus 1
1.1 Brownian Motion 1
1.2 Stochastic Integrals 7
1.3 Stochastic Di erentials and Ito's Lemma 11
1.4 Multi-Factor Extensions 16
1.5 Martingales 19
2 The Martingale Representation Theorem 23
2.1 Changing Measures with Binomial Models 23
2.2 Change of Measures under Brownian Filtration 29
2.3 The Martingale Representation Theorem 32
2.4 A Complete Market with Two Securities 33
2.5 Replicating and Pricing of Contingent Claims 34
2.6 Multi-Factor Extensions 36
2.7 A Complete Market with Multiple Securities 37
2.8 The Black{Scholes Formula 41
2.9 Notes 43
3 Interest Rates and Bonds 51
3.1 Interest Rates and Fixed-Income Instruments 51
3.2 Yields 57
3.3 Zero-Coupon Bonds and Zero-Coupon Yields 61
3.4 Forward Rates and Forward-Rate Agreements 64
3.5 Yield-Based Bond Risk Management 65
4 The Heath{Jarrow{Morton Model 71
4.1 Lognormal Model: The Starting Point 72
4.2 The HJM Model 75
4.3 Special Cases of the HJM Model 78
4.4 Estimating the HJM Model from Yield Data 82
4.5 A Case Study with a Two-Factor Model 92
4.6 Monte Carlo Implementations 93
4.7 Forward Prices 96
4.8 Forward Measure 99
4.9 Black's Formula for Call and Put Options 102
4.10 Numeraires and Changes of Measure 109
4.11 Linear Gaussian Models 110
4.12 Notes 111
5 Short-Rate Models and Lattice Implementation 119
5.1 From Short-Rate Models to Forward-Rate Models 120
5.2 General Markovian Models 122
5.3 Binomial Trees of Interest Rates 131
5.4 A General Tree-Building Procedure 138
6 The LIBOR Market Model 149
6.1 LIBOR Market Instruments 149
6.2 The LIBOR Market Model 162
6.3 Pricing of Caps and Floors 167
6.4 Pricing of Swaptions 168
6.5 Speci cations of the LIBOR Market Model 175
6.6 Monte Carlo Simulation Method 178
6.7 Notes 185
7 Calibration of LIBOR Market Model 189
7.1 Implied Cap and Caplet Volatilities 190
7.2 Calibrating the LIBOR Market Model to Caps 192
7.3 Calibration to Caps, Swaptions, and Input Correlations 195
7.4 Calibration Methodologies 200
7.5 Sensitivity with Respect to the Input Prices 223
8 Volatility and Correlation Adjustments 225
8.1 Adjustment due to Correlations 226
8.2 Adjustment due to Convexity 234
8.3 Timing Adjustment 243
8.4 Quanto Derivatives 244
8.5 Notes 249
9 Ane Term Structure Models 253
9.1 An Exposition with One-Factor Models 254
9.2 Analytical Solution of Riccarti Equations 261
9.3 Pricing Options on Coupon Bonds 265
9.4 Distributional Properties of Square-Root Processes 266
9.5 Multi-Factor Models 266
9.6 Swaption Pricing under ATSMs 272
9.7 Notes 278
10 Market Models with Stochastic Volatilities 281
10.1 SABR Model 282
10.2 The Wu and Zhang (2001) Model 289
10.3 Pricing of Caplets 293
10.4 Pricing of Swaptions 297
10.5 Model Calibration 301
10.6 Notes 308
11 Levy Market Model 315
11.1 Introduction to Levy Processes 315
11.2 The Levy HJM Model 323
11.3 Market Model under Levy Processes 328
11.4 Caplet Pricing 330
11.5 Swaption Pricing 332
11.6 Approximate Swaption Pricing via the Merton Formula 334
11.7 Notes 336
12 Market Model for In
ation Derivatives Modeling 343
12.1 CPI Index and In
ation Derivatives Market 345
12.2 Rebuilt Market Model and the New Paradigm 349
12.3 Pricing In
ation Derivatives 356
12.4 Model Calibration 360
12.5 Smile Modeling 361
12.6 Notes 362
13 Market Model for Credit Derivatives 363
13.1 Pricing of Risky Bonds: A New Perspective 365
13.2 Forward Spreads 367
13.3 Two Kinds of Default Protection Swaps 369
13.4 Par CDS Rates 371
13.5 Implied Survival Curve and Recovery-Rate Curve 373
13.6 Credit Default Swaptions and an Extended Market Model 378
13.7 Pricing of CDO Tranches under the Market Model 384
13.8 Notes 391
14 Dual-Curve SABR-LMM Market Model for Post-Crisis Interest Rate Derivatives Markets 393
14.1 LIBOR Market Model under Default Risks 395
14.2 Swaps and Basis Swaps 401
14.3 Option Pricing Using Heat Kernel Expansion 403
14.4 Pricing 3M Swaptions 421
14.5 Pricing Caps and Swaptions of Other Tenors 436
14.6 Notes 442
15 xVA: De nition, Evaluation, and Risk Management 449
15.1 Pricing through Bilateral Replications 453
15.2 The Rise of Other xVA 459
15.3 Examples 466
15.4 Notes 468
References 471
Index 489
Series: Chapman and Hall/CRC Financial Mathematics Series
Pages: 518 pages
Publisher: CRC Press; 2 edition (February 25, 2019)
Language: English
ISBN-10: 0815378912
ISBN-13: 978-0815378914
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