金融模型中的鞅方法 第2版 英文2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

金融模型中的鞅方法 第2版 英文PDF格式电子书版下载

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PartⅠ Spot and Futures Markets3

1 AnIntroduction to Financial Derivatives3

1.1 Options3

1.2 Futures Contracts and Options5

1.3 Forward Contracts6

1.4 Call and Put Spot Options8

1.4.1 One-period Spot Market9

1.4.2 Replicating Portfolios10

1.4.3 Martingale Measure for a Spot Market12

1.4.4 Absence of Arbitrage13

1.4.5 Optimality of Replication15

1.4.6 Change of a Numeraire17

1.4.7 Put Option18

1.5 Forward Contracts19

1.5.1 Forward Price20

1.6 Futures Call and Put Options21

1.6.1 Futures Contracts and Futures Prices21

1.6.2 One-period Futures Market22

1.6.3 Martingale Measure for a Futures Market23

1.6.4 Absence of Arbitrage24

1.6.5 One-period Spot/Futures Market26

1.7 Options of American Style26

1.8 Universal No-arbitrage Inequalities31

2 Discrete-time Security Markets35

2.1 TheCox-Ross-Rubinstein Model36

2.1.1 Binomial Lattice for the Stock Price36

2.1.2 Recursive Pricing Procedure38

2.1.3 CRR Option Pricing Formula43

2.2 Martingale Properties of the CRR Model46

2.2.1 Martingale Measures47

2.2.2 Risk-neutral Valuation Formula50

2.2.3 Change of a Numeraire51

2.3 The Black-Scholes Option Pricing Formula53

2.4 Valuation of American Options58

2.4.1 American Call Options58

2.4.2 American Put Options60

2.4.3 American Claims61

2.5 Options on a Dividend-paying Stock63

2.6 Security Markets in Discrete Time65

2.6.1 Finite Spot Markets66

2.6.2 Self-financing Trading Strategies66

2.6.3 Replication and Arbitrage Opportunities68

2.6.4 Arbitrage Price69

2.6.5 Risk-neutral Valuation Formula70

2.6.6 Existence ofa Martingale Measure73

2.6.7 Completeness of a Finite Market75

2.6.8 Separating Hyperplane Theorem77

2.6.9 Change of a Numeraire78

2.6.10 Discrete-time Models with Infinite State Space79

2.7 Finite Futures Markets80

2.7.1 Self-financing Futures Strategies81

2.7.2 Martingale Measures for a Futures Market82

2.7.3 Risk-neutral Valuation Formula84

2.7.4 Futures Prices Versus Forward Prices85

2.8 American Contingent Claims87

2.8.1 Optimal Stopping Problems90

2.8.2 Valuation and Hedging of American Claims97

2.8.3 American Call and Put101

2.9 Game Contingent Claims101

2.9.1 Dynkin Games102

2.9.2 Valuation and Hedging ofGame Contingent Claims108

3 Benchmark Models in Continuous Time113

3.1 The Black-Scholes Model114

3.1.1 Risk-free Bond114

3.1.2 Stock Price114

3.1.3 Self-financing Trading Strategies118

3.1.4 Martingale Measure for the Black-Scholes Model120

3.1.5 Black-Scholes Option Pricing Formula125

3.1.6 Case of Time-dependent Coefficients131

3.1.7 Merton's Model132

3.1.8 Put-Call Parity for Spot Options134

3.1.9 Black-Scholes PDE134

3.1.10 A Riskless Portfolio Method137

3.1.11 Black-Scholes Sensitivities140

3.1.12 Market Imperfections144

3.1.13 Numerical Methods145

3.2 A Dividend-paying Stock147

3.2.1 Case of a Constant Dividend Yield148

3.2.2 Case of Known Dividends151

3.3 Bachelier Model154

3.3.1 Bachelier Option Pricing Formula155

3.3.2 Bachelier's PDE157

3.3.3 Bachelier Sensitivities158

3.4 Black Model159

3.4.1 Self-financing Futures Strategies160

3.4.2 Martingale Measure for the Futures Market160

3.4.3 Black's Futures Option Formula161

3.4.4 Options on Forward Contracts165

3.4.5 Forward and Futures Prices167

3.5 Robustness of the Black-Scholes Approach168

3.5.1 Uncertain Volatility168

3.5.2 European Call and Put Options169

3.5.3 Convex Path-independent European Claims172

3.5.4 General Path-independent European Claims177

4 Foreign Market Derivatives181

4.1 Cross-currency Market Model181

4.1.1 Domestic Martingale Measure182

4.1.2 Foreign Martingale Measure184

4.1.3 Foreign Stock Price Dynamics185

4.2 Currency Forward Contracts and Options186

4.2.1 Forward Exchange Rate186

4.2.2 Currency Option Valuation Formula187

4.3 Foreign Equity Forward Contracts191

4.3.1 Forward Price of a Foreign Stock191

4.3.2 Quanto Forward Contracts192

4.4 Foreign Market Futures Contracts194

4.5 Foreign Equity Options197

4.5.1 Options Struck in a Foreign Currency198

4.5.2 Options Struck in Domestic Currency199

4.5.3 Quanto Options200

4.5.4 Equity-linked Foreign Exchange Options202

5 American Options205

5.1 Valuation of American Claims206

5.2 American Call and PutOptions213

5.3 Early Exercise Representation of an American Put216

5.4 Analytical Approach219

5.5 Approximations ofthe American Put Price222

5.6 Option on a Dividend-paying Stock224

5.7 Game Contingent Claims226

6 Exotic Options229

6.1 Packages230

6.2 Forward-start Options231

6.3 Chooser Options232

6.4 Compound Options233

6.5 Digital Options234

6.6 Barrier Options235

6.7 Lookback Options238

6.8 Asian Options242

6.9 Basket Options245

6.10 Quantile Options249

6.11 Other Exotic Options251

7 Volatility Risk253

7.1 Implied Volatilities of Traded Options254

7.1.1 Historical Volatility255

7.1.2 Implied Volatility255

7.1.3 Implied Volatility Versus Historical Volatility256

7.1.4 Approximate Formulas257

7.1.5 Implied Volatility Surface259

7.1.6 Asymptotic Behavior of the Implied Volatility261

7.1.7 Marked-to-Market Models264

7.1.8 Vega Hedging265

7.1.9 Correlated Brownian Motions267

7.1.10 Forward-start Options269

7.2 Extensions ofthe Black-Scholes Model273

7.2.1 CEV Model273

7.2.2 Shifted Lognormal Models277

7.3 Local Volatility Models278

7.3.1 Implied Risk-Neutral Probability Law278

7.3.2 Local Volatility281

7.3.3 Mixture Models287

7.3.4 Advantages and Drawbacks of LV Models290

7.4 Stochastic Volatility Models291

7.4.1 PDE Approach292

7.4.2 Examples of SV Models293

7.4.3 Hull and White Model294

7.4.4 Heston's Model299

7.4.5 SABRModel301

7.5 Dynamical Models of Volatility Surfaces302

7.5.1 Dynamics ofthe Local Volatility Surface303

7.5.2 Dynamics ofthe Implied Volatility Surface303

7.6 Alternative Approaches307

7.6.1 Modelling of Asset Returns308

7.6.2 Modelling of Volatility and Realized Variance313

8 Continuous-time Security Markets315

8.1 Standard MarketModels316

8.1.1 Standard Spot Market316

8.1.2 Futures Market325

8.1.3 Choice of a Numeraire327

8.1.4 Existence of a Martingale Measure330

8.1.5 Fundamental Theorem of Asset Pricing332

8.2 Multidimensional Black-Scholes Model333

8.2.1 Market Completeness335

8.2.2 Variance-minimizing Hedging337

8.2.3 Risk-minimizing Hedging338

8.2.4 Market Imperfections345

PartⅡ Fixed-income Markets351

9 Interest Rates and Related Contracts351

9.1 Zero-coupon Bonds351

9.1.1 Term Structure of Interest Rates352

9.1.2 Forward Interest Rates353

9.1.3 Short-term Interest Rate354

9.2 Coupon-bearing Bonds354

9.2.1 Yield-to-Maturity355

9.2.2 Market Conventions357

9.3 Interest Rate Futures358

9.3.1 Treasury Bond Futures358

9.3.2 Bond Options359

9.3.3 Treasury Bill Futures360

9.3.4 Eurodollar Futures362

9.4 Interest Rate Swaps363

9.4.1 Forward Rate Agreements364

9.5 Stochastic Models ofBond Prices366

9.5.1 Arbitrage-free Family of Bond Prices366

9.5.2 Expectations Hypotheses367

9.5.3 Case of It？ Processes368

9.5.4 Market Price for Interest Rate Risk371

9.6 Forward Measure Approach372

9.6.1 Forward Price373

9.6.2 Forward Martingale Measure375

9.6.3 Forward Processes378

9.6.4 Choice of a Numeraire379

10 Short-Term Rate Models383

10.1 Single-factor Models384

10.1.1 Time-homogeneous Models384

10.1.2 Time-inhomogeneous Models394

10.1.3 Model Choice399

10.1.4 American Bond Options401

10.1.5 Options on Coupon-beating Bonds402

10.2 Multi-factor Models402

10.2.1 State Variables403

10.2.2 Affine Models404

10.2.3 Yield Models404

10.3 Extended CIR Model406

10.3.1 Squared Bessel Process407

10.3.2 Model Construction407

10.3.3 Change ofa Probability Measure408

10.3.4 Zero-coupon Bond409

10.3.5 Case of Constant Coefficients410

10.3.6 Case of Piecewise Constant Coefficients411

10.3.7 Dynamics of Zero-coupon Bond412

10.3.8 Transition Densities414

10.3.9 Bond Option415

11 Models of Instantaneous Forward Rates417

11.1 Heath-Jarrow-Morton Methodology418

11.1.1 Ho and Lee Model419

11.1.2 Heath-Jarrow-Morton Model419

11.1.3 Absence of Arbitrage421

11.1.4 Short-term Interest Rate427

11.2 Gaussian HJM Model428

11.2.1 Markovian Case430

11.3 European Spot Options434

11.3.1 Bond Options435

11.3.2 Stock Options438

11.3.3 Option on a Coupon-bearing Bond441

11.3.4 Pricing of General Contingent Claims444

11.3.5 Replication of Options446

11.4 Volatilities and Correlations449

11.4.1 Volatilities449

11.4.2 Correlations451

11.5 Futures Price452

11.5.1 Futures Options453

11.6 PDE Approach to Interest Rate Derivatives457

11.6.1 PDEs for Spot Derivatives457

11.6.2 PDEs for Futures Derivatives461

11.7 Recent Developments465

12 Market LIBOR Models469

12.1 Forward and Futures LIBORs471

12.1.1 One-period Swap Settled in Arrears471

12.1.2 One-period Swap Settled in Advance473

12.1.3 Eurodollar Futures474

12.1.4 LIBOR in the Gaussian HJM Model475

12.2 Interest Rate Caps and Floors477

12.3 Valuation in the Gaussian HJM Model479

12.3.1 Plain-vanilla Caps and Floors479

12.3.2 Exotic Caps481

12.3.3 Captions483

12.4 LIBOR Market Models484

12.4.1 Black's Formula for Caps484

12.4.2 Miltersen,Sandmann and Sondermann Approach486

12.4.3 Brace,Gatarek and Musiela Approach486

12.4.4 Musiela and Rutkowski Approach489

12.4.5 SDEs for LIBORs under the Forward Measure492

12.4.6 Jamshidian's Approach495

12.4.7 Altemative Derivation of Jamshidian's SDE498

12.5 Properties of the Lognormal LIBOR Model500

12.5.1 Transition Density of the LIBOR501

12.5.2 Transition Density of the Forward Bond Price503

12.6 Valuation in the Lognormal LIBOR Model506

12.6.1 Pricing of Caps and Floors506

12.6.2 Hedging of Caps and Floors508

12.6.3 Valuation of European Claims510

12.6.4 Bond Options513

12.7 Extensions of the LLM Model515

13 Alternative Market Models517

13.1 Swaps and Swaptions518

13.1.1 Forward Swap Rates518

13.1.2 Swaptions522

13.1.3 Exotic Swap Derivatives524

13.2 Valuarion in the Gaussian HJM Model527

13.2.1 Swaptions527

13.2.2 CMS Spread Options527

13.2.3 Yield Curve Swaps529

13.3 Co-terminal Forward Swap Rates530

13.3.1 Jamshidian's Model535

13.3.2 Valuation of Co-terminal Swaptions538

13.3.3 Hedging of Swaptions539

13.3.4 Bermudan Swaptions540

13.4 Co.initial Forward Swap Rates541

13.4.1 Valuation of Co-initial Swaptions544

13.4.2 Valuation of Exotic Options545

13.5 Co.sliding Forward Swap Rates546

13.5.1 Modelling of Co-sliding Swap Rates547

13.5.2 Valuation of Co-sliding Swaptions551

13.6 Swap Rate Model Versus LIBOR Model552

13.6.1 Swaptions in the LLM Model553

13.6.2 Caplets in the Co-terminal Swap Market Model557

13.7 Markov-functional Models558

13.7.1 Terminal Swap Rate Model559

13.7.2 Calibration of Markov-functional Models562

13.8 Fiesaker and Hughston Approach565

13.8.1 Rational Lognormal Model568

13.8.2 Valuation of Caps and Swaptions569

14 Cross-currency Derivatives573

14.1 Arbitrage-free Cross-currency Markets574

14.1.1 Forward Price of a Foreign Asset576

14.1.2 Valuation of Foreign Contingent Claims580

14.1.3 Cross-currency Rates581

14.2 Gaussian Model581

14.2.1 Currency Options582

14.2.2 Foreign Equity Options583

14.2.3 Cross-currency Swaps588

14.2.4 Cross-currency Swaptions599

14.2.5 Basket Caps602

14.3 Model of Forward LIBOR Rates603

14.3.1 Quamo Cap604

14.3.2 Cross-currency Swap606

14.4 Concluding Remarks607

PartⅢ APPENDIX611

A An Overview of It？ Stochastic Calculus611

A.1 Conditional Expectation611

A.2 Filtrations and Adapted Processes615

A.3 Martingales616

A.4 Standard Brownian Motion617

A.5 Stopping Times and Martingales621

A.6 It？ Stochastic Integral622

A.7 Continuous Local Martingales625

A.8 Continuous Semimartingales628

A.9 It？'s Lemma630

A.10 Lévy's Characterization Theorem633

A.11 Martingale Representation Property634

A.12 Stochastic Differential Equations636

A.13 Stochastic Exponential639

A.14 Radon-Nikodym Density640

A.15 Girsanov's Theorem641

A.16 Martingale Measures645

A.17 Feynman-Kac Forrnula646

A.18 First Passage Times649

References657

Index707