Dynamic Term Structure Modeling: The Fixed Income Valuation Course & CD-ROM / Edition 1

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Praise for Dynamic Term Structure Modeling

"This book offers the most comprehensive coverage of term-structure models I have seen so far, encompassing equilibrium and no-arbitrage models in a new framework, along with the major solution techniques using trees, PDE methods, Fourier methods, and approximations. It is an essential reference for academics and practitioners alike."
—Sanjiv Ranjan Das Professor of Finance, Santa Clara University, California, coeditor, Journal of Derivatives

"Bravo! This is an exhaustive analysis of the yield curve dynamics. It is clear, pedagogically impressive, well presented, and to the point."
—Nassim Nicholas Taleb author, Dynamic Hedging and The Black Swan

"Nawalkha, Beliaeva, and Soto have put together a comprehensive, up-to-date textbook on modern dynamic term structure modeling. It is both accessible and rigorous and should be of tremendous interest to anyone who wants to learn about state-of-the-art fixed income modeling. It provides many numerical examples that will be valuable to readers interested in the practical implementations of these models."
—Pierre Collin-Dufresne Associate Professor of Finance, UC Berkeley

"The book provides a comprehensive description of the continuous time interest rate models. It serves an important part of the trilogy, useful for financial engineers to grasp the theoretical underpinnings and the practical implementation."
—Thomas S. Y. Ho, PHD President, Thomas Ho Company, Ltd, coauthor, The Oxford Guide to Financial Modeling

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Product Details

  • ISBN-13: 9780471737148
  • Publisher: Wiley, John & Sons, Incorporated
  • Publication date: 5/4/2007
  • Series: Wiley Finance Series , #180
  • Edition description: Includes CD-ROM
  • Edition number: 1
  • Pages: 683
  • Product dimensions: 6.46 (w) x 9.33 (h) x 2.27 (d)

Meet the Author

Sanjay K. Nawalkha, PhD, is an Associate Professor of Finance at the Isenberg School of Management, University of Massachusetts Amherst, where he teaches graduate courses in finance theory and fixed income. He has published extensively in academic and practitioner journals, and is the President and founder of Nawalkha and Associates—a fixed income training and consulting firm.

Natalia A.Beliaeva, PhD, is an Assistant Professor of Finance at the Sawyer Business School, Suffolk University, Boston. She also holds a master's degree in computer science (artificial intelligence) from the University of Massachusetts Amherst. Dr. Beliaeva's expertise is in the area of applied numerical methods for pricing fixed income derivatives.

Gloria M.Soto, PhD, is a Professor of Applied Economics and Finance at the University of Murcia, Spain, where she teaches courses in financial markets and institutions and applied economics. Dr. Soto has published extensively in both Spanish and international journals in finance and economics, especially in the areas of interest rate risk management and related fixed income topics.

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Table of Contents

List of Figures     xxxi
List of Tables     xxxv
A Simple Introduction to Continuous-Time Stochastic Processes     1
Continuous-Time Diffusion Processes     3
Wiener Process     3
Ito Process     5
Ito's Lemma     7
Simple Rules of Stochastic Differentiation and Integration     9
Obtaining Unconditional Mean and Variance of Stochastic Integrals under Gaussian Processes     9
Examples of Gaussian Stochastic Integrals     11
Mixed Jump-Diffusion Processes     14
The Jump-Diffusion Process     14
Ito's Lemma for the Jump-Diffusion Process     15
Arbitrage-Free Valuation     17
Arbitrage-Free Valuation: Some Basic Results     18
A Simple Relationship between Zero-Coupon Bond Prices and Arrow Debreu Prices     20
The Bayes Rule for Conditional Probabilities of Events     20
The Relationship between Current and Future AD Prices     21
The Relationship between Cross-Sectional AD Prices and Intertemporal Term Structure Dynamics     22
Existence of the Risk-Neutral Probability Measure     23
Stochastic Discount Factor     28
Radon-Nikodym Derivative     30
Arbitrage-Free Valuation inContinuous Time     31
Change of Probability Measure under a Continuous Probability Density     32
The Girsanov Theorem and the Radon-Nikodym Derivative     34
Equivalent Martingale Measures     35
Stochastic Discount Factor and Risk Premiums     43
The Feynman-Kac Theorem     43
Valuing Interest Rate and Credit Derivatives: Basic Pricing Frameworks     49
Eurodollar and Other Time Deposit Futures     54
Valuing Futures on a Time Deposit     58
Convexity Bias     60
Treasury Bill Futures     61
Valuing T-Bill Futures     62
Convexity Bias     63
Treasury Bond Futures     64
Conversion Factor     65
Cheapest-to-Deliver Bond     67
Options Embedded in T-Bond Futures     68
Valuing T-Bond Futures     68
Treasury Note Futures     72
Forward Rate Agreements     73
Interest Rate Swaps     74
Day-Count Conventions     76
The Financial Intermediary     77
Motivations for Interest Rate Swaps     78
Pricing Interest Rate Swaps     82
Interest Rate Swaptions     85
Caps and Floors      88
Caplet     90
Floorlet     91
Collarlet     92
Caps, Floors, and Collars     92
Black Implied Volatilities for Caps and Swaptions     93
Black Implied Volatilities: Swaptions     95
Black Implied Volatilities: Caplet     96
Black Implied Volatilities: Caps     97
Black Implied Volatilities: Difference Caps     98
Pricing Credit Derivatives Using the Reduced-Form Approach     98
Default Intensity and Survival Probability     100
Recovery Assumptions     101
Risk-Neutral Valuation under the RMV Assumption     102
Risk-Neutral Valuation under the RFV Assumption     103
Valuing Credit Default Swaps Using the RFV Assumption     104
A New Taxonomy of Term Structure Models     106
Fundamental and Preference-Free Single-Factor Gaussian Models     113
The Arbitrage-Free Pricing Framework of Vasicek     115
The Term Structure Equation     116
Risk-Neutral Valuation     118
The Fundamental Vasicek Model     120
Bond Price Solution     124
Preference-Free Vasicek+, Vasicek++, and Vasicek+++ Models     128
The Vasicek+ Model      128
The Vasicek++, or the Extended Vasicek Model     136
The Vasicek+++, or the Fully Extended Vasicek Model     140
Valuing Futures     144
Valuing Futures under the Vasicek, Vasicek+ and Vasicek++ Models     145
Valuing Futures under the Vasicek+++ Model     150
Valuing Options     153
Options on Zero-Coupon Bonds     153
Options on Coupon Bonds     157
Valuing Interest Rate Contingent Claims Using Trees     161
Binomial Trees     163
Trinomial Trees     165
Trinomial Tree under the Vasicek++ Model: An Example     171
Trinomial Tree under the Vasicek+++ Model: An Example     178
Bond Price Solution Using the Risk-Neutral Valuation Approach under the Fundamental Vasicek Model and the Preference-Free Vasicek+ Model     181
Hull's Approximation to Convexity Bias under the Ho and Lee Model     184
Fundamental and Preference-Free Jump-Extended Gaussian Models     187
Fundamental Vasicek-GJ Model     188
Bond Price Solution     191
Jump-Diffusion Tree     194
Preference-Free Vasicek-GJ+ and Vasicek-GJ++ Models     201
The Vasicek-GJ+ Model     202
The Vasicek-GJ++ Model     203
Jump-Diffusion Tree     205
Fundamental Vasicek-EJ Model     206
Bond Price Solution     207
Jump-Diffusion Tree     209
Preference-Free Vasicek-EJ++ Model     216
Jump-Diffusion Tree     218
Valuing Futures and Options     218
Valuing Futures     219
Valuing Options: The Fourier Inversion Method     222
Probability Transformations with a Damping Constant     233
The Fundamental Cox, Ingersoll, and Ross Model with Exponential and Lognormal Jumps     237
The Fundamental Cox, Ingersoll, and Ross Model     239
Solution to Riccati Equation with Constant Coefficients     242
CIR Bond Price Solution     243
General Specifications of Market Prices of Risk     244
Valuing Futures     245
Valuing Options     248
Interest Rate Trees for the Cox, Ingersoll, and Ross Model     250
Binomial Tree for the CIR Model     250
Trinomial Tree for the CIR Model     263
Pricing Bond Options and Interest Rate Options with Trinomial Trees     273
The CIR Model Extended with Jumps     279
Valuing Futures     283
Futures on a Time Deposit     284
Valuing Options      285
Jump-Diffusion Trees for the CIR Model Extended with Jumps     287
Exponential Jumps     287
Lognormal Jumps     295
Preference-Free CIR and CEV Models with Jumps     305
Mean-Calibrated CIR Model     307
Preference-Free CIR+ and CIR++ Models     309
A Common Notational Framework     312
Probability Density and the Unconditional Moments     313
Bond Price Solution     315
Expected Bond Returns     317
Constant Infinite-Maturity Forward Rate under Explosive CIR+ and CIR++ Models     318
A Comparison with Other Markovian Preference-Free Models     321
Calibration to the Market Prices of Bonds and Interest Rate Derivatives     322
Valuing Futures     323
Valuing Options     325
Interest Rate Trees     327
The CIR+ and CIR++ Models Extended with Jumps     328
Preference-Free CIR-EJ+ and CIR-EJ++ Models     329
Jump-Diffusion Trees     331
Fundamental and Preference-Free Constant-Elasticity-of-Variance Models     331
Forward Rate and Bond Return Volatilities under the CEV++ Models     333
Valuing Interest Rate Derivatives Using Trinomial Trees     336
Fundamental and Preference-Free Constant-Elasticity-of-Variance Models with Lognormal Jumps     341
Fundamental and Preference-Free Two-Factor Affine Models     345
Two-Factor Gaussian Models     348
The Canonical, or the Ac, Form: The Dai and Singleton [2002] Approach     349
The Ar Form: The Hull and White [1996] Approach     353
The Ay Form: The Brigo and Mercuric [2001, 2006] Approach     356
Relationship between the A[subscript 0c](2)++ Model and the A[subscript 0y](2)++ Model     358
Relationship between the A[subscript 0r](2)++ Model and the A[subscript 0y](2)++ Model     360
Bond Price Process and Forward Rate Process     361
Probability Density of the Short Rate     362
Valuing Options     363
Two-Factor Gaussian Trees     364
Two-Factor Hybrid Models     373
Bond Price Process and Forward Rate Process     377
Valuing Futures     377
Valuing Options     380
Two-Factor Stochastic Volatility Trees     382
Two-Factor Square-Root Models     393
The Ay Form     393
The Ar Form     399
Relationship between the Canonical Form and the Ar Form     402
Two-Factor "Square-Root" Trees     403
Hull and White Solution of [eta](t, T)     410
Fundamental and Preference-Free Multifactor Affine Models     413
Three-Factor Affine Term Structure Models     416
The A[subscript 1r](3), A[subscript 1r](3)+, and A[subscript 1r](3)++ Models     416
The A[subscript 2r](3), A[subscript 2r](3)+, and A[subscript 2r](3)++ Models     421
Simple Multifactor Affine Models with Analytical Solutions     425
The Simple A[subscript M](N) Models     425
The Simple A[subscript M](N)+ and A[subscript M](N)++ Models     427
The Nested ATSMs     429
Valuing Futures     429
Valuing Options on Zero-Coupon Bonds or Caplets: The Fourier Inversion Method     433
Valuing Options on Coupon Bonds or Swaptions: The Cumulant Expansion Approximation     435
Calibration to Interest Rate Caps Data     448
Unspanned Stochastic Volatility     455
Multifactor ATSMs for Pricing Credit Derivatives     457
Simple Reduced-Form ATSMs under the RMV Assumption     458
Simple Reduced-Form ATSMs under the RFV Assumption     468
The Solution of [eta](t, T, [phiv]) for CDS Pricing Using Simple A[subscript M](N) Models under the RFV Assumption     476
Stochastic Volatility Jump-Based Mixed-Sign A[subscript N](N)-EJ++ Model and A[subscript 1](3)-EJ++ Model      477
The Mixed-Sign A[subscript N](N)-EJ++ Model     478
The A[subscript 1](3)-EJ++Model     479
Fundamental and Preference-Free Quadratic Models     483
Single-Factor Quadratic Term Structure Model     484
Duration and Convexity     488
Preference-Free Single-Factor Quadratic Model     492
Forward Rate Volatility     495
Model Implementation Using Trees     497
Extension to Jumps     498
Fundamental Multifactor QTSMs     501
Bond Price Formulas under Q[subscript 3](N) and Q[subscript 4](N) Models     505
Parameter Estimates     506
Preference-Free Multifactor QTSMs     508
Forward Rate Volatility and Correlation Matrix     515
Valuing Futures     518
Valuing Options on Zero-Coupon Bonds or Caplets: The Fourier Inversion Method     524
Valuing Options on Coupon Bonds or Swaptions: The Cumulant Expansion Approximation     527
Calibration to Interest Rate Caps Data     531
Multifactor QTSMs for Valuing Credit Derivatives     537
Reduced-Form Q[subscript 3](N), Q[subscript 3](N)+, and Q[subscript 3](N)++ Models under the RMV Assumption     537
Reduced-Form Q[subscript 3](N) and Q[subscript 3](N)+ Models under the RFV Assumption     543
The Solution of [eta](t, T, [phiv]) for CDS Pricing Using the Q[subscript 3](N) Model under the RFV Assumption     547
The HJM Forward Rate Model     551
The HJM Forward Rate Model     552
Numerical Implementation Using Nonrecombining Trees     556
A One-Factor Nonrecombining Binomial Tree     557
A Two-Factor Nonrecombining Trinomial Tree     565
Recursive Programming     569
A Recombining Tree for the Proportional Volatility HJM Model     572
Forward Price Dynamics under the Forward Measure     573
A Markovian Forward Price Process under the Proportional Volatility Model     575
A Recombining Tree for the Proportional Volatility Model Using the Nelson and Ramaswamy Transform     576
The LIBOR Market Model     583
The Lognormal Forward LIBOR Model (LFM)     585
Multifactor LFM under a Single Numeraire     588
The Lognormal Forward Swap Model (LSM)     591
A Joint Framework for Using Black's Formulas for Pricing Caps and Swaptions     595
The Relationship between the Forward Swap Rate and Discrete Forward Rates     596
Approximating the Black Implied Volatility of a Swaption under the LFM     597
Specifying Volatilities and Correlations      600
Forward Rate Volatilities: Some General Results     600
Forward Rate Volatilities: Specific Functional Forms     604
Instantaneous Correlations and Terminal Correlations     608
Full-Rank Instantaneous Correlations     612
Reduced-Rank Correlation Structures     619
Terminal Correlations     623
Explaining the Smile: The First Approach     623
The CEV Extension of the LFM     624
Displaced-Diffusion Extension of the LFM     626
Unspanned Stochastic Volatility Jump Models     629
Joshi and Rebonato [2003] Model     630
Jarrow, Li, and Zhao [2007] Model     631
An Extension of the JLZ Model     636
Empirical Performance of the JLZ [2007] Model     637
Reference     647
About the CD-ROM     658
Index     661
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