CONTENTS

Preface xv

Acknowledgments xix

About tbe Autbor xxi

1 SWAPSANDFlXEDINCOMEINSTRUMENTS 11.1 Eurodollar Futures 21.2 Treasury Bilis and Bonds 3

Hedging with T-BiIIFutures 6Long Futures Hedge: Hedging Synthetic Futures on I82-Day T-BiII 7

1.3 Computing Treasury BiII Prices and Yields in Matlab 101.4 Hedging Debt Positions 11

Hedging a Future 91-Day T-BiII Investment with T-BiII Call 11Short Hedge: Managing the Maturity Gap 12Maturity Gap and the Carrying Cost Model 14

Managing the Maturity Gap with Eurodollar Put 14Short Hedge: Hedging a Variable-Rate Loan 15

1.5 Bond and Swap Duration, Modified Duration, and DVOl 18Hedging Bond Portfolios 20

1.6 Term Structure of Rates 241.7 Bootstrap Method 25

1.8 Bootstrapping in Matlab 281.9 Bootstrapping in Excel 301.10 General Swap Pricing in Matlab 33

Description 431.11 Swap Pricing in Matlab Using Term Structure Analysis 451.12 Swap Valuation in C++ 501.13 Bermudan Swaption Pricing in Matlab 61

Endnotes 65vii

viii Contents

2 COPULA FUNCTIONS 672.1 Definitionand BasicPropertiesof CopulaFunctions 672.2 Classesof CopulaFunctions 69

MultivariateGaussianCopula 69MultivariateStudent's T Copula 71

2.3 ArchimedeanCopulae 732.4 CalibratingCopulae 74

ExactMaximumLikelihoodMethod(EML) 74

The InferenceFunctionsfor MarginsMethod(IFM) 76The CanonicalMaximumLike1ihoodMethod(CML) 76

2.5 NumericalResultsforCalibratingReal-MarketData 77Bouye,Durrelman,Nikeghbali,Riboulet,and RoncalliMethod 77MashalandZeeviMethod 82

2.6 UsingCopulasin Excel 86Endnotes 87

3 MORTGAGE-BACKEDSECURITIES 913.1 PrepaymentModels 933.2 NumericalExampleof PrepaymentModel 953.3 MBSPricingandQuoting 983.4 PrepayrnentRisk andAverageLife of MBS 1003.5 MBSPricingUsingMonteCarioin C++ 1113.6 MatlabFixed-IncorneToolkitfor MBSValuation 1263.7 CollateralizedMortgageObligations(CMOs) 1313.8 CMOImplernentationin C++ 1373.9 PlannedArnortizationClasses(PACS) 1463.10 Principal-and Interest-On1yStrips 1493.11 InterestRate Risk 1513.12 DynamicHedgingofMBS 151

The MultivariableDensityEstirnationMethod 153Endnotes 160

4 COLLATERALlZED DEBT OBLIGATIONS 1634.1 Structureof CDOs 164

CashFlowCDOs 165MarketValueCDOs 166BalanceSheetCashFlowsCDOs 166ArbitrageCDOs 166ArbitrageMarketValueCDOs 166

Contents Contents ix

67 Arbitrage Cash Flow CDOs 16767 Credit Enhancement in Cash Flow Transactions 16769 Credit Enhancement in Market Value Transactions: Advance Rates69 and the Over-Collateralization Test 16771 Minimum Net Worth Test 16973 Transaction Characteristics 17174 4.2 Synthetic CDOs 17174 Fully Funded Synthetic CDOs 17776 Partially and Unfunded Funded Synthetic CDOs 17976 4.3 Balance Sheet Management with CDS 18177 4.4 The Distribution of Default Losses on a Portfolio 181

od 77 4.5 CDO Equity Tranche 18682 CDO Equity Tranche Performance 18686 The CDO Embedded Option 18787The Price of Equity 188

91 Using Moody's Binomial Expansion Technique to Structure

93 Synthetic CDOs 18995 Correlation Risk of CDO Tranches 19398 4.6 CDO Tranche Pricing 196

100 4.7 Pricing Equation 197111 4.8 Simulation Algorithm 197126 4.9 CDO Pricing in Matlab 199131 4.10 CDO Pricing in C++ 208137 4.11 CD02 Pricing 216146 4.12 Fast Loss Calculation for CDOs and CD02s 216149 Fast AIgorithm for Computing CDO Tranche Loss in Matlab 218151 Endnotes 220151153 5 CREDIT DERIVATIVES 223160 5.1 Credit Default Swaps 224

5.2 CDS Day Counting Conventions 226163164 5.3 General Valuation of Credit Default Swaps 226165 5.4 Hazard Rate Function 228166 5.5 Poisson and Cox Processes 229166 5.6 Valuation Using a Deterministic Intensity Model 232166 5.7 Hazard Rate Function Calibration 235166 5.8 Credit Curve Construction and Calibration 248

Contents

x

5.9 Credit Basket Default Swaps Prieing 249Generation of Correlated Default Stopping Times 250Sampling from Elliptieal Copulae 250The Distribution of Default Arrival Times 252

Basket CDS Pricing AIgorithm 252

5.10 Credit Basket Prieing in Matlab 2555.11 Credit Basket Prieing in C++ 2645.12 Credit Linked Notes (CLNs) 291

CLNs with Collateralized Loan or Bond Obligations (CLOs or CBOs) 295

Prieing Tranched Credit Linked Notes 296Regulatory Capital 296

Endnotes 297

6 WEATHERDERlVATIVES 2996.1 Weather Derivatives Market 3006.2 Weather Contraets 303

CME Weather Futures 303

6.3 Modeling Temperature 306Noise Proeess 308Mean-Reversion 309

6.4 Pararneter Estimation 3106.5 Volatility Estimation 3106.6 Mean-Reversion Pararneter Estirnation 311

6.7 Pricing Weather Derivatives 312ModelFrarnework 312Pricing a Heating Degree Day Option 313

6.8 Historical Burn Analysis 3166.9 Time-Series Wealher Forecasting 3186.10 Prieing Weather Options in C++ 328

Endnotes 330

7 ENERGY AND POWER DERlVATIVES 3337.1 Electricity Markets 3347.2 E!eerricity Pricing Mode!s 336

Modeling the Price Process 336One-Factor Model 337Estimating the Deterministie Component 340Estimation of the Stochastic Process for the One-Factor Mode!s 34!

Two-Factor Model 342

Contents Contents xi

249 7.3 Swing Options 344

250 7.4 The Longstaff-Schwartz Algorithm for American and Bermudan Options 345

250 The LSM Algorithm 346252 7.5 Extension of Longstaff-Schwartz to Swing Options 348

252 7.6 General Case: Upswings, Downswings, and Penalty Functions 351255 7.7 Swing Option Pricing in Mat1ab 352264 7.8 LSM Simu1ation Results 352291 Upper and Lower Boundaries 354

orCBOs) 295 Exercise Strategies 356296 The Threshold of Early Exercise 358296 Interplay Between Early Exercise and Option Value 360297 7.9 Pricing of Energy Cornmodity Derivatives 362

Cross-Cornmodity Spread Options 362299Modell 364

300Model2 365

303Model3 366

3037.10 Jump Diffusion Pricing Models 368306

308Model la: Affine Mean-Reverting Jump-Diffusion Process 368

309Model1b 369

310 Model 2a: Time- Varying Drift Component 370

310 Model 2b: Time- Varying Version of Model 1b 372

311 7.11 Stochastic Vo1atility Pricing Models 372

312 Model3a: Two-Factor Jump-DiffusionAffine Process with StochasticVolatility 372

3127.12 Model Parameter Estimation 373

313ML-CCF Estimators

316 375

318ML-MCCF Estimators 376

328Spectral GMM Estimators 379

330Simulation 383

7.13 Pararneter Estimation in Matlab 385333 7.14 Energy Cornmodity Mode1s 385334 7.15 Natural Gas 387336 Natural Gas Markets 387336 Natural Gas Spot Prices 389337 7.16 Gas Pricing Mode1s 390340 One-Factor Model 390

lodels 341 Two- Factor Mode1 391342 Calibration 393

xiiContents

One-Faetor Model CalibrationTwo-Factor Model Calibration

7.17 Natural Gas Prieing in Matlab7.18 Natural Gas and Eleetrieity Swaps

GeneratorEnd User

Endnotes

393394398398400401402

8 PRICING POWER DERIVATIVES: THEORY AND MATLABIMPLEMENTATION 4078.1 Introduetion 407

8.2 Power Markets 409

8.3 Traditional Valuation Approaehes Are Prob1ematie for Power 410

8.4 Fundamentals-Based Mode1s 413

8.5 The PJ Mode1-0verview 415

8.6 Model Calibration 419

8.7 Using the Calibrated Model to Priee Options 423

Daily Strike Options 423

Monthly Strike Options 423

Spark Spread Options 424

8.8 Option Valuation Methodology 424

Splitting the (Finite) Differenee: Dai1y Strike and Month1yStrike Options 424

Matlab Implementation for a Monthly Strike Option 426

Spark Spread Options 434

Matlab Implementation of Spark Spread Option Valuation 434

8.9 Results 439

8.10 Summary 443

Endnotes 443

References 445

9 COMMERCIAL REAL ESTATE ASSET-BACKED SECURITIES 4479.1 Introduetion 447

9.2 Motivations for Asset-Backed Securitization 4499.3 Coneepts of Seeuritizing Real Estate Cash Flows 450

9.4 Commercial Real Estate-Backed Seeuritization (CREBS)-Singapore'sExperience 452

9.5 Strueture of a Typical CREBS 456

A CREBS Case by Visor Limited 457

Contents

393394398398400401402

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424426434434439443443445

~s 447447449450

Singapore's452456457

Contents xiii

9.6 Pricing of CREBS 459Swaps and Swaptions 459The Cash Flow Swap Structure for CREBS 459

9.7 Valuation of CREBS Using a Swap Framework 460Basic Swap Valuation Framework 460Pricing of Credit Risks for CREBS Using the Proposed Swap Mode! 461Modeling Defau!t Risks in the CREBS Swap 461

9.8 Numerical Analysis of Default Risks for a Typical CREBS 463Monte CarIo Simu!ation Process 463Input Parameters 464Analysis of Results 465

9.9 Matlab Code for the Numerical Analysis 4679.10 Summary 470

Endnotes 470

A INTEREST RATE TREE MODELING IN MATLAB 473A.I BDT Modeling in Matlab 473A.2 Hull-WhiteTrees in Matlab 478A.3 Black-Karasinski Trees in Matlab 486AA HJM Pricing in Matlab 490

Description 492Syntax 493Arguments 493Examp!es 493Creating an HJM Vo!atility and Pricing Mode! 494

A.5 Matlab Exce! Link Examp!e 497A.6 Two-Factor HJM Mode! Imp!ementation in Matlab 500

Endnotes 501

B CHAPTER 7 CODE 503

REFERENCES 543

INDEX 555