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Preface vii
Theory and Applications of Derivatives Modeling 1
Introduction to Counterparty Credit Risk 3
Credit Charge, Credit Benefit, and Credit Premium 8
Credit Cost, Accrued Funding Cost, and Accrued Funding Benefit 14
Trading Strategies and Opportunities 17
Comparison with Bond Credit Risk 28
Prevailing Strategies for Counterparty Credit Risk Management 30
Wrong-way and Right-way Exposures or Trades 33
Introduction to Modeling and Pricing of Counterparty Credit Risk 35
Martingale Arbitrage Pricing in Real Market 37
Basics of Arbitrage 38
Arbitrage Opportunity and Arbitrage Pricing 38
Self Financing Trading Strategies and Arbitrage 42
Subtleties in Arbitrage Pricing in Real Market 45
Counterparty Credit Risk 45
The Risk-free Interest Rate 45
Bid/Ask Spread 49
Un-hedgeable Variables 51
Primary Model Calibration and Secondary Model Calibration 53
Models for Pricing, Models for Hedging, and Hedging Calibration 56
Incomplete Market and Completing the Market 60
Arbitrage Models and Non-arbitrageModels 61
Arbitrage Models and Non-arbitrage Models 61
Financial Market Participants and Financial Activities 63
Trading Opportunities and Strategies 66
Simple Bonds and IR Swaps 68
Callable Bonds and Cancelable IR Swaps 72
Examples of Practical Complications 73
Structured Notes and Exotic Derivatives 74
IR/FX Hybrid Notes and Derivatives 79
Asset Swaps and Repackaging 82
Credit Hybrid Derivatives 82
Capital Structure Arbitrage 84
Quasi-arbitrage Opportunities 86
Why Should Derivatives Instruments Exist 87
Martingale Arbitrage Modeling 89
Harrison-Pliska Martingale No-arbitrage Theorem 89
Martingale Derivatives Pricing in a Binomial Economy 91
Harrison-Pliska Martingale No-arbitrage Theorem for Assets with Intermediate Cashflows or Income 96
Foundation for Arbitrage Pricing 97
Examples of Martingales and Equivalent Martingale Measures 98
Martingale Representation and SDE for Derivatives Pricing 101
Change of Probability Measure and Importance Sampling 109
PDF for Derivatives Pricing and P&L Decomposition 113
SABR Stochastic Volatility Model 118
An Example of Martingale Modeling in Real Market 119
Problems 122
The Black-Scholes Framework and Extensions 123
More on Martingale Models 123
Single State Variable and Single Numeraire 124
Single State Variable and Multiple Numeraires 133
Black's Model 142
Put-Call Parity Revised 143
Replication Model 147
Impact of Volatility Skews and Smiles on Hedge Ratios and Hedging Strategies 149
Other Extensions of Black-Scholes Framework 152
Martingale Resampling and Interpolation 153
Martingale Interpolation 159
Brownian Bridge Interpolation 164
Moment Matching in One-factor Case 167
Quadratic Resampling 168
Moment Matching for All Odd Moments and Kurtosis 168
Moment Matching for Higher Order Moments 172
Conditional Quadratic Resampling 174
Moment Matching in Multi-factor Case 178
Martingale Resampling 180
Unconditional Martingale Resampling at the State Variable Level 181
Conditional Martingale Resampling at the State Variable Level 192
Brownian Bridge Resampling at the State Variable Level 197
Martingale Control Variate at the Underlying Instrument Level 198
Martingale Resampling at the Derivatives Price Level 200
Application to Secondary Model Calibration 202
Other Applications of Martingale Resampling 203
Modeling of Multiple Indices 204
JLT Risk Neutralization of Credit Rating Transition Process 205
Calibration of Credit Spread Processes 208
Risk Neutralization of Mortgage Prepayment Model 210
Accuracy and Precision Tests 210
Examples of Numerical Results 210
Introduction to Interest Rate Term Structure Modeling 212
Interest Rate Models Classification 212
Short Rate Models 213
Gaussian Short Rate Models 214
Lognormal Short Rate Models 215
Constant Elasticity of Variance Models 215
Affine Models and Quadratic Models 215
What Interest Rate Models Should One Use? 216
The Heath-Jarrow-Morton Framework 218
The Heath-Jarrow-Morton Model 218
The Ritchken-Sankarasubramanian Model 224
The Inui-Kijima Model 228
Overview of Numerical Implementations of the RS and the IK Model 234
Recombining Trinomial Tree Technique 234
Adaptive Recombining Trinomial Tree Technique 239
Overview of Applications of the Adaptive Trinomial Tree Technique to the RS Model and the IK Model 241
Appendix 242
Closed-form Solutions for the RS Model 242
Closed-form Solutions for the IK Model 246
The Interest Rate Market Model 249
BGM Model versus HJM Model 250
The Brace-Gatarek-Musiela Original Approach 252
Comparison Between HJM and BGM Models 256
Jamshidian's Approach 258
Martingale Approach 259
The LIBOR Market Model and the Black Formula for Caps/Floors 259
The Swap Market Model and the Black Formula for European Swaptions 266
Overview of Simultaneous and Globally Consistent Pricing and Hedging 273
Simultaneous Consistent Pricing Through Approximation 275
More on Simultaneous Consistent Pricing 279
More on the Martingale or Full-dimensional LIBOR Market Model 283
Modeling Interest Rate Volatility Skew and Smile 287
CEV and LCEV Models for Modeling the Volatility Skew 288
Examples of Volatility Skew for Caplets and Swaptions 290
The Nonexploding Bushy Tree Technique 292
Construction of a Nonexploding Bushy Tree 294
Modeling Stochastic Processes on a Nonexploding Bushy Tree 297
Application of Martingale Control Variate Technique 301
Numerical Results 303
General Framework for Multi-factor Modeling for Hybrid Market 312
Stochastic Volatility BGM Models 314
Examples of Stochastic Volatility BGM Model Results 316
Appendix 317
More Numerical Results Obtained With the NBT Technique 317
Sufficient Conditions for Convergence 319
Application of Girsanov's Change of Measure Theorem to Derivation of the Martingale or Full-dimensional LIBOR Market Model 323
Credit Risk Modeling and Pricing 327
Pricing Simple Defaultable Instruments 328
Default Contingent Instruments 334
A Simple Markov Chain Model 335
Modeling Correlated Default Event Processes with a Factor Model 341
Modeling Correlated Default Time Processes with the Copula Approach 348
Recovery Rate Modeling 350
Risky Market Model for Credit Spread Modeling 351
Joint Credit Spread and Default Modeling 359
Counterparty Credit Risk Pricing in OTC Derivatives 362
Credit Charge Calculation 365
Expected and Potential Exposures and Expected Shortfall 366
Credit Benefit Calculation 368
Collateral or Margin Agreement 369
Net Credit Charge and Funding Spread Calculation 370
Martingale Relationships in Credit Charge Calculations 372
Closed-form Solutions and Approximations 374
Framework for Counterparty Credit Risk Modeling and Pricing 378
Centralized Market Process Modeling and Scenario Generation Engine 380
Exposure or MTM Modeling Engine 380
New Trade and Real-time Exposure or MTM Modeling Engine 382
Counterparty Credit Process Modeling and Scenario Generation Engine 383
Portfolio Effect Handling and Aggregation Engine 383
Counterparty Credit Risk Pricing Engine 384
Sensitivity and Scenario Analysis Engine 384
Unexpected Risk Modeling Engine 385
Interest Rate Market Fundamentals and Proprietary Trading Strategies 387
Simple Interest Rate Products 389
Treasury Issues 389
Treasury Bills 389
Treasury Notes and Bonds 390
Futures Contracts 391
Euro-dollars and LIBOR 392
Euro-dollar Futures 392
Note and Bond Futures 393
Interest Rate Derivatives 394
Interest Rate Swaps 394
Plain Vanilla Interest Rate Swap 394
Forward Swap 395
Basis Swap 395
Constant Maturity Swap 395
Swaption 395
Bond Options 396
OTC Options 396
Yield Curve Modeling 397
Introduction 397
The Bootstrap Method 398
Orthogonal Exponential Spline Model 399
Exponential Basis Functions 400
Maximum Likelihood Estimates for Spline Coefficients 403
Implementation of the Spline Model 405
Summary 406
Swap Curve 406
Constructing Euro-dollar Strip Curve 407
Convexity Adjustment 408
Two-Factor Risk Model 411
PCA and TFRM Methodologies 411
Principal Components Analysis 413
Two-factor Risk Model Specification 418
Empirical Validation 421
Applications 423
Level-hedged Bullet/Barbell Trades 423
Two-factor Portfolio Hedging Strategy 423
Bond Indices with Level and Curve Risk Profile 426
Adjusted Durations 427
[Beta]-Adjusted Duration 430
Hedging the Extremely Long End 432
Future Directions 433
The Holy Grail - Two-Factor Interest Rate Arbitrage 434
Profit, Loss, and Financing Costs 434
Two-factor Arbitrage 435
Trading Strategy 437
Yield Decomposition Model 440
Volatility Adjusted Duration 441
Dollar Value of Convexity 442
Expected Total Rate of Return 443
Measurement of Risk Premium 444
Expectation Curve 445
Expected FED Funds Rate 447
Yield Decomposition Analysis 447
Discussion 448
Inflation Linked Instruments Modeling 450
Inflation Swaps 451
Functions and Applications 452
Asset/Liability Management 453
Inflation Swaps as Hedging and Trading Instruments 453
Investment Alternatives 453
Inflation Linked Debt Issuance 454
Complementary to Interest Rate Swaps 454
Inflation Swap Level 455
Real Rate Swap Curve 456
Zero-coupon Inflation Swap Curve Valuation Methods 457
Risk Measures and Hedging 458
Prospect of the Inflation Swap Business 460
Interest Rate Proprietary Trading Strategies 461
Rich/Cheap Trade 462
Rich/Cheap Analysis 464
Yield Curve Sector Rich/Cheap Analysis 464
Rich/Cheap Analysis for Notes and Bonds 466
Bond/Swap Trade 468
Curvature Trade 469
Spread Trade 470
Box Trade 472
OAT Floater Trade 472
Cash/Futures Trade 473
A Generic Convergence Trading Strategy 473
Other Factors Related to Trading Strategy 476
Transaction Cost 476
Higher Risk and Highly Profitable Trades 411
Bet Big When All Components Line Up 478
Human Judgment 478
References 479
Index 491
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