论波动率模型 英文2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

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1．General Introduction,Changing Volatility Models and European Options Pricing1.1 General Introduction1

1.2 Introduction to Changing Volatility Models4

1.3 Model Completeness and European Option Pricing4

1.4 Single Period Volatility Changing Problems9

1.4.1 Fixed Volatility Changing Time with Barrier B9

1.4.2 Random Volatility Changing Time with a Hitting Barrier B14

1.5 Multi-Period Volatility Changing Problems15

1.6 Extension to Incomplete Market19

1.6.1 A Simple Random Volatility Changing Model-Extension to Stochastic Volatility Model19

1.6.2 Future Research20

1.7 Appendix:Proof20

1.7.1 Proof of Proposition 1.120

1.7.2 Proof of Proposition 1.223

1.7.3 Proof of Proposition 1.324

1.7.4 Proof of Proposition 1.426

1.7.5 Proof of Proposition 1.527

1.7.6 Proof of Proposition 1.629

1.7.7 Theorem 2.2 of[132]:Uniqueness of the Equivalent Martingale Measure30

2．Introduction to Stochastic Volatility and Local Stochastic Volatility Models2.1 Stochastic Volatility Models-A General Set-Up31

2.1.1 Model Set-Up31

2.1.2 Change of Measure and Model Incompleteness32

2.2 Making the Stochastic Volatility Economy Complete34

2.3 European Option Price36

2.4 Local Stochastic Volatility Models:An Introduction38

2.5 Adjustment to the Calculation of Greeks in a Non-Constant Implied Volatility Model42

3．Foreign Exchange Options with Local Stochastic Volatility and Stochastic Interest Rates3.1 Introduction44

3.2 The FX-IR Hybrid Model46

3.3 Asymptotic Expansion50

3.3.1 A Brief Introduction50

3.3.2 European Option Pricing and Implied Volatility50

3.4 Model Implementation and Numerical Results58

3.5 FX Option Pricing via Fourier Transform under Stochastic Interest Rates,Stochastic Volatility and the Jump Process66

3.5.1 The Multi-Factor Model66

3.5.2 Change of Measure and Option Pricing67

3.5.3 Model Implementation70

3.5.4 Calibration Results for the USD/JPY Market72

3.6 Perfect Hedging with Stochastic Interest Rates and Local Stochastic Volatility75

3.6.1 Hedging with Options76

3.6.2 Hedging with Options and Bonds80

3.7 Partial Hedging with Hedging Error Analysis82

3.7.1 Hedging with One Option for the Volatility Risk83

3.7.2 Hedging with One Option for the Interest Rate Risk85

3.8 Model Mis-specification and Hedging Error Analysis86

3.8.1 Delta Hedging Difference between the CEV and CEV-SV Models86

3.8.2 Model Mis-specification:The Importance of Stochastic Interest Rates88

3.9 Application to Power-Reverse-Dual-Currency Notes91

3.9.1 PRDC-TARN:The Structured Product91

3.9.2 Smile Impact on PRDC-TARN Product Valuation93

3.10 Conclusion and Future Research95

3.11 Appendix:Proof96

3.11.1 Derivation of the European Option Formula96

3.11.2 Conditional Expectations of the Multiple Weiner-Ito Integral101

3.11.3 Watanabe Theorem104

3.11.4 The European Option Formula from the Fourier Transform Method105

4．Non-Biased Monte Carlo Simulation for a Heston-Type Stochastic Volatility Model4.1 Introduction107

4.2 Properties of the Square Root Process108

4.3 Simulation of Vt:Application of the Saddle Point Method111

4.4 Simulation of ∫t+△ t Vs ds given Vt and Vt+△:Moment Matching Technique112

4.5 Simulation of Ft+△t given Ft113

4.6 Conclusion and Future Research114

4.7 Appendix:Proof114

4.7.1 Characteristic Function and Moments of the Square Root Process114

4.7.2 The Lugannani and Rice Formula for the Cumulative Distribution Function116

5．The LIBOR Market Model with Stochastic Volatility and Jump Processes5.1 Introduction118

5.2 The LIBOR Forward Rate Model121

5.2.1 Risk-Neutral Measure121

5.2.2 Change of Measure123

5.3 The LIBOR Swap Rate Model124

5.3.1 The Swap Market124

5.3.2 Change of Measure125

5.4 Caplet and Swaption Pricing Via Fourier Transform128

5.4.1 Caplet Pricing128

5.4.2 Swaption Pricing130

5.5 Conclusion and Future Research132

5.6 Appendix:Proof133

5.6.1 Proof of Lemma 5.1133

5.6.2 Proof of Proposition 5.2134

5.6.3 Proof of Proposition 5.3136

5.6.4 Proof of Proposition 5.4137

5.6.5 The Marked Point Process138

5.6.6 The Girsanov Theorem and Ito's Lemma on Jump Processes The Girsanov Theorem for Jump Processes139

5.6.7 The Derivation of Characteristic Functions Caplet142

Bibliography146