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

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This book addresses selected practical applications and recent developments in the areas of quantitative financial modeling in derivatives instruments, some of which are from the authors' own research and practice. While the primary scope of this book is the fixed-income market (with further focus on the interest rate market), many of the methodologies presented also apply to other financial markets, such as the credit, equity, and foreign exchange markets.

This book, which assumes that the reader is familiar with the basics of stochastic calculus and derivatives modeling, is written from the point of view of financial engineers or practitioners, and, as such, it puts more emphasis on the practical applications of financial mathematics in the real market than the mathematics itself with precise (and tedious) technical conditions. It attempts to combine economic insights with mathematics and modeling so as to help the reader develop intuitions.

In addition, the book addresses the counterparty credit risk modeling, pricing, and arbitraging strategies, which are relatively recent developments and are of increasing importance. It also discusses various trading structuring strategies and touches upon some popular credit/IR/FX hybrid products, such as PRDC, TARN, Snowballs, Snowbears, CCDS, credit extinguishers.
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Product Details

  • ISBN-13: 9789810240790
  • Publisher: World Scientific Publishing Company, Incorporated
  • Publication date: 10/28/2006
  • Pages: 520
  • Product dimensions: 6.00 (w) x 9.10 (h) x 1.30 (d)

Table of Contents

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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