Quantitative Analysis, Derivatives Modeling, and Trading Strategies : In the Presence of Counterparty Credit Risk for the Fixed-Income Market

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Format: Hardcover
Pub. Date: 2007-01-23
Publisher(s): WORLD SCIENTIFIC PUB CO INC
List Price: $175.00

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Summary

This book addresses many practical issues in the fixed-income market, some of which are quite important, yet not readily available in the literature in an integral and systematic form. The topics covered include: (l) yield curve models, such as the orthogonal exponential spline model, the two-factor risk model, and the yield decomposition model; (2) actual trading strategies used by leading Wall Street power houses, and forecasting models, such as artificial neural networks; (3) dynamic interest rate modeling and derivative pricing in the Heath-Jarrow-Morton framework with particular emphasis on the Brace-Gatarek-Musiela interest rate market model, as well as practical multi-factor numerical implementations using, for example, the non-exploding bushy tree technique; (4) introduction to value-at-risk analysis. The book attempts to combine simplicity and economic insights with mathematical elegance, and it will be beneficial to both novice and advanced readers who work or are interested in the fixed-income market.

Table of Contents

Prefacep. vii
Theory and Applications of Derivatives Modelingp. 1
Introduction to Counterparty Credit Riskp. 3
Credit Charge, Credit Benefit, and Credit Premiump. 8
Credit Cost, Accrued Funding Cost, and Accrued Funding Benefitp. 14
Trading Strategies and Opportunitiesp. 17
Comparison with Bond Credit Riskp. 28
Prevailing Strategies for Counterparty Credit Risk Managementp. 30
Wrong-way and Right-way Exposures or Tradesp. 33
Introduction to Modeling and Pricing of Counterparty Credit Riskp. 35
Martingale Arbitrage Pricing in Real Marketp. 37
Basics of Arbitragep. 38
Arbitrage Opportunity and Arbitrage Pricingp. 38
Self Financing Trading Strategies and Arbitragep. 42
Subtleties in Arbitrage Pricing in Real Marketp. 45
Counterparty Credit Riskp. 45
The Risk-free Interest Ratep. 45
Bid/Ask Spreadp. 49
Un-hedgeable Variablesp. 51
Primary Model Calibration and Secondary Model Calibrationp. 53
Models for Pricing, Models for Hedging, and Hedging Calibrationp. 56
Incomplete Market and Completing the Marketp. 60
Arbitrage Models and Non-arbitrage Modelsp. 61
Arbitrage Models and Non-arbitrage Modelsp. 61
Financial Market Participants and Financial Activitiesp. 63
Trading Opportunities and Strategiesp. 66
Simple Bonds and IR Swapsp. 68
Callable Bonds and Cancelable IR Swapsp. 72
Examples of Practical Complicationsp. 73
Structured Notes and Exotic Derivativesp. 74
IR/FX Hybrid Notes and Derivativesp. 79
Asset Swaps and Repackagingp. 82
Credit Hybrid Derivativesp. 82
Capital Structure Arbitragep. 84
Quasi-arbitrage Opportunitiesp. 86
Why Should Derivatives Instruments Existp. 87
Martingale Arbitrage Modelingp. 89
Harrison-Pliska Martingale No-arbitrage Theoremp. 89
Martingale Derivatives Pricing in a Binomial Economyp. 91
Harrison-Pliska Martingale No-arbitrage Theorem for Assets with Intermediate Cashflows or Incomep. 96
Foundation for Arbitrage Pricingp. 97
Examples of Martingales and Equivalent Martingale Measuresp. 98
Martingale Representation and SDE for Derivatives Pricingp. 101
Change of Probability Measure and Importance Samplingp. 109
PDF for Derivatives Pricing and P&L Decompositionp. 113
SABR Stochastic Volatility Modelp. 118
An Example of Martingale Modeling in Real Marketp. 119
Problemsp. 122
The Black-Scholes Framework and Extensionsp. 123
More on Martingale Modelsp. 123
Single State Variable and Single Numerairep. 124
Single State Variable and Multiple Numerairesp. 133
Black's Modelp. 142
Put-Call Parity Revisedp. 143
Replication Modelp. 147
Impact of Volatility Skews and Smiles on Hedge Ratios and Hedging Strategiesp. 149
Other Extensions of Black-Scholes Frameworkp. 152
Martingale Resampling and Interpolationp. 153
Martingale Interpolationp. 159
Brownian Bridge Interpolationp. 164
Moment Matching in One-factor Casep. 167
Quadratic Resamplingp. 168
Moment Matching for All Odd Moments and Kurtosisp. 168
Moment Matching for Higher Order Momentsp. 172
Conditional Quadratic Resamplingp. 174
Moment Matching in Multi-factor Casep. 178
Martingale Resamplingp. 180
Unconditional Martingale Resampling at the State Variable Levelp. 181
Conditional Martingale Resampling at the State Variable Levelp. 192
Brownian Bridge Resampling at the State Variable Levelp. 197
Martingale Control Variate at the Underlying Instrument Levelp. 198
Martingale Resampling at the Derivatives Price Levelp. 200
Application to Secondary Model Calibrationp. 202
Other Applications of Martingale Resamplingp. 203
Modeling of Multiple Indicesp. 204
JLT Risk Neutralization of Credit Rating Transition Processp. 205
Calibration of Credit Spread Processesp. 208
Risk Neutralization of Mortgage Prepayment Modelp. 210
Accuracy and Precision Testsp. 210
Examples of Numerical Resultsp. 210
Introduction to Interest Rate Term Structure Modelingp. 212
Interest Rate Models Classificationp. 212
Short Rate Modelsp. 213
Gaussian Short Rate Modelsp. 214
Lognormal Short Rate Modelsp. 215
Constant Elasticity of Variance Modelsp. 215
Affine Models and Quadratic Modelsp. 215
What Interest Rate Models Should One Use?p. 216
The Heath-Jarrow-Morton Frameworkp. 218
The Heath-Jarrow-Morton Modelp. 218
The Ritchken-Sankarasubramanian Modelp. 224
The Inui-Kijima Modelp. 228
Overview of Numerical Implementations of the RS and the IK Modelp. 234
Recombining Trinomial Tree Techniquep. 234
Adaptive Recombining Trinomial Tree Techniquep. 239
Overview of Applications of the Adaptive Trinomial Tree Technique to the RS Model and the IK Modelp. 241
Appendixp. 242
Closed-form Solutions for the RS Modelp. 242
Closed-form Solutions for the IK Modelp. 246
The Interest Rate Market Modelp. 249
BGM Model versus HJM Modelp. 250
The Brace-Gatarek-Musiela Original Approachp. 252
Comparison Between HJM and BGM Modelsp. 256
Jamshidian's Approachp. 258
Martingale Approachp. 259
The LIBOR Market Model and the Black Formula for Caps/Floorsp. 259
The Swap Market Model and the Black Formula for European Swaptionsp. 266
Overview of Simultaneous and Globally Consistent Pricing and Hedgingp. 273
Simultaneous Consistent Pricing Through Approximationp. 275
More on Simultaneous Consistent Pricingp. 279
More on the Martingale or Full-dimensional LIBOR Market Modelp. 283
Modeling Interest Rate Volatility Skew and Smilep. 287
CEV and LCEV Models for Modeling the Volatility Skewp. 288
Examples of Volatility Skew for Caplets and Swaptionsp. 290
The Nonexploding Bushy Tree Techniquep. 292
Construction of a Nonexploding Bushy Treep. 294
Modeling Stochastic Processes on a Nonexploding Bushy Treep. 297
Application of Martingale Control Variate Techniquep. 301
Numerical Resultsp. 303
General Framework for Multi-factor Modeling for Hybrid Marketp. 312
Stochastic Volatility BGM Modelsp. 314
Examples of Stochastic Volatility BGM Model Resultsp. 316
Appendixp. 317
More Numerical Results Obtained With the NBT Techniquep. 317
Sufficient Conditions for Convergencep. 319
Application of Girsanov's Change of Measure Theorem to Derivation of the Martingale or Full-dimensional LIBOR Market Modelp. 323
Credit Risk Modeling and Pricingp. 327
Pricing Simple Defaultable Instrumentsp. 328
Default Contingent Instrumentsp. 334
A Simple Markov Chain Modelp. 335
Modeling Correlated Default Event Processes with a Factor Modelp. 341
Modeling Correlated Default Time Processes with the Copula Approachp. 348
Recovery Rate Modelingp. 350
Risky Market Model for Credit Spread Modelingp. 351
Joint Credit Spread and Default Modelingp. 359
Counterparty Credit Risk Pricing in OTC Derivativesp. 362
Credit Charge Calculationp. 365
Expected and Potential Exposures and Expected Shortfallp. 366
Credit Benefit Calculationp. 368
Collateral or Margin Agreementp. 369
Net Credit Charge and Funding Spread Calculationp. 370
Martingale Relationships in Credit Charge Calculationsp. 372
Closed-form Solutions and Approximationsp. 374
Framework for Counterparty Credit Risk Modeling and Pricingp. 378
Centralized Market Process Modeling and Scenario Generation Enginep. 380
Exposure or MTM Modeling Enginep. 380
New Trade and Real-time Exposure or MTM Modeling Enginep. 382
Counterparty Credit Process Modeling and Scenario Generation Enginep. 383
Portfolio Effect Handling and Aggregation Enginep. 383
Counterparty Credit Risk Pricing Enginep. 384
Sensitivity and Scenario Analysis Enginep. 384
Unexpected Risk Modeling Enginep. 385
Interest Rate Market Fundamentals and Proprietary Trading Strategiesp. 387
Simple Interest Rate Productsp. 389
Treasury Issuesp. 389
Treasury Billsp. 389
Treasury Notes and Bondsp. 390
Futures Contractsp. 391
Euro-dollars and LIBORp. 392
Euro-dollar Futuresp. 392
Note and Bond Futuresp. 393
Interest Rate Derivativesp. 394
Interest Rate Swapsp. 394
Plain Vanilla Interest Rate Swapp. 394
Forward Swapp. 395
Basis Swapp. 395
Constant Maturity Swapp. 395
Swaptionp. 395
Bond Optionsp. 396
OTC Optionsp. 396
Yield Curve Modelingp. 397
Introductionp. 397
The Bootstrap Methodp. 398
Orthogonal Exponential Spline Modelp. 399
Exponential Basis Functionsp. 400
Maximum Likelihood Estimates for Spline Coefficientsp. 403
Implementation of the Spline Modelp. 405
Summaryp. 406
Swap Curvep. 406
Constructing Euro-dollar Strip Curvep. 407
Convexity Adjustmentp. 408
Two-Factor Risk Modelp. 411
PCA and TFRM Methodologiesp. 411
Principal Components Analysisp. 413
Two-factor Risk Model Specificationp. 418
Empirical Validationp. 421
Applicationsp. 423
Level-hedged Bullet/Barbell Tradesp. 423
Two-factor Portfolio Hedging Strategyp. 423
Bond Indices with Level and Curve Risk Profilep. 426
Adjusted Durationsp. 427
[Beta]-Adjusted Durationp. 430
Hedging the Extremely Long Endp. 432
Future Directionsp. 433
The Holy Grail - Two-Factor Interest Rate Arbitragep. 434
Profit, Loss, and Financing Costsp. 434
Two-factor Arbitragep. 435
Trading Strategyp. 437
Yield Decomposition Modelp. 440
Volatility Adjusted Durationp. 441
Dollar Value of Convexityp. 442
Expected Total Rate of Returnp. 443
Measurement of Risk Premiump. 444
Expectation Curvep. 445
Expected FED Funds Ratep. 447
Yield Decomposition Analysisp. 447
Discussionp. 448
Inflation Linked Instruments Modelingp. 450
Inflation Swapsp. 451
Functions and Applicationsp. 452
Asset/Liability Managementp. 453
Inflation Swaps as Hedging and Trading Instrumentsp. 453
Investment Alternativesp. 453
Inflation Linked Debt Issuancep. 454
Complementary to Interest Rate Swapsp. 454
Inflation Swap Levelp. 455
Real Rate Swap Curvep. 456
Zero-coupon Inflation Swap Curve Valuation Methodsp. 457
Risk Measures and Hedgingp. 458
Prospect of the Inflation Swap Businessp. 460
Interest Rate Proprietary Trading Strategiesp. 461
Rich/Cheap Tradep. 462
Rich/Cheap Analysisp. 464
Yield Curve Sector Rich/Cheap Analysisp. 464
Rich/Cheap Analysis for Notes and Bondsp. 466
Bond/Swap Tradep. 468
Curvature Tradep. 469
Spread Tradep. 470
Box Tradep. 472
OAT Floater Tradep. 472
Cash/Futures Tradep. 473
A Generic Convergence Trading Strategyp. 473
Other Factors Related to Trading Strategyp. 476
Transaction Costp. 476
Higher Risk and Highly Profitable Tradesp. 411
Bet Big When All Components Line Upp. 478
Human Judgmentp. 478
Referencesp. 479
Indexp. 491
Table of Contents provided by Ingram. All Rights Reserved.

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