利率衍生物定价的有效方法 英文PDF|Epub|txt|kindle电子书版本网盘下载

利率衍生物定价的有效方法 英文PDF格式电子书版下载

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1．Introduction1

2．Arbitrage,Martingales and Numerical Methods5

2.1 Arbitrage and Martingales6

2.1.1 Basic Setup6

2.1.2 Equivalent Martingale Measure8

2.1.3 Change of Numeraire Theorem10

2.1.4 Girsanov's Theorem and It？'s Lemma11

2.1.5 Application：Black-Scholes Model12

2.1.6 Application：Foreign-Exchange Options14

2.2 Numerical Methods16

2.2.1 Derivation of Black-Scholes Partial Differential Equation16

2.2.2 Feynman-Kac Formula17

2.2.3 Numerical Solution of PDE's18

2.2.4 Monte Carlo Simulation18

2.2.5 Numerical Integration20

Part Ⅰ．Spot and Forward Rate Models23

3．Spot and Forward Rate Models23

3.1 Vasicek Methodology23

3.1.1 Spot Interest Rate23

3.1.2 Partial Differential Equation24

3.1.3 Calculating Prices25

3.1.4 Example：Ho-Lee Model26

3.2 Heath-Jarrow-Morton Methodology27

3.2.1 Forward Rates27

3.2.2 Equivalent Martingale Measure28

3.2.3 Calculating Prices29

3.2.4 Example：Ho-Lee Model30

3.3 Equivalence of the Methodologies30

4．Fundamental Solutions and the Forward-Risk-Adjusted Measure31

4.1 Forward-Risk-Adjusted Measure32

4.2 Fundamental Solutions34

4.3 Obtaining Fundamental Solutions36

4.4 Example：Ho-Lee Model37

4.4.1 Radon-Nikodym Derivative37

4.4.2 Fundamental Solutions38

4.5 Fundamental Solutions for Normal Models40

5．The Hull-White Model45

5.1 Spot Rate Process46

5.1.1 Partial Differential Equation47

5.1.2 Transformation of Variables47

5.2 Analytical Formul？48

5.2.1 Fundamental Solutions49

5.2.2 Option Prices50

5.2.3 Prices for Other Instruments51

5.3 Implementation of the Model52

5.3.1 Fitting the Model to the Initial Tern-Structure52

5.3.2 Transformation of Variables53

5.3.3 Trinomial Tree53

5.4 Performance of the Algorithm55

5.5 Appendix57

6．The Squared Gaussian Model59

6.1 Spot Rate Process60

6.1.1 Partial Differential Equation60

6.2 Analytical Formul？61

6.2.1 Fundamental Solutions62

6.2.2 Option Prices63

6.3 Implementation of the Model64

6.3.1 Fitting the Model to the Initial Term-Structure64

6.3.2Trinomial Tree66

6.4 Appendix A66

6.5 Appendix B69

7．An Empirical Comparison of One-Factor Models71

7.1 Yield-Curve Models72

7.2 Econometric Approach74

7.3 Data77

7.4 Empirical Results77

7.5 Conclusions84

Part Ⅱ．Market Rate Models87

8．LIBOR and Swap Market Models87

8.1 LIBOR Market Models88

8.1.1 LIBOR Process88

8.1.2 Caplet Price89

8.1.3 Terminal Measure90

8.2 Swap Market Models91

8.2.1 Interest Rate Swaps92

8.2.2 Swaption Price93

8.2.3 Terminal Measure95

8.2.4 T1-Forward Measure96

8.3 Monte Carlo Simulation for LIBOR Market Models97

8.3.1 Calculating the Numeraire Rebased Payoff98

8.3.2 Example：Vanilla Cap99

8.3.3 Discrete Barrier Caps/Floors100

8.3.4 Discrete Barrier Digital Caps/Floors102

8.3.5 Payment Stream103

8.3.6 Ratchets103

8.4 Monte Carlo Simulation for Swap Market Models104

8.4.1 Terminal Measure104

8.4.2 T1-Forward Measure105

8.4.3 Example：Spread Option106

9． Markov-Functional Models109

9.1 Basic Assumptions110

9.2 LIBOR Markov-Functional Model111

9.3 Swap Markov-Functional Model114

9.4 Numerical Implementation115

9.4.1 Numerical Integration115

9.4.2 Non-Parametric Implementation117

9.4.3 Semi-Parametric Implementation118

9.5 Forward Volatilities and Auto-Correlation120

9.5.1 Mean-Reversion and Auto-Correlation120

9.5.2 Auto-Correlation and the Volatility Function121

9.6 LIBOR Example：Barrier Caps121

9.6.1 Numerical Calculation121

9.6.2 Comparison with LIBOR Market Model123

9.6.3 Impact of Mean-Reversion124

9.7 LIBOR Example：Chooser-and Auto-Caps125

9.7.1 Auto-Caps/Floors125

9.7.2 Chooser-Caps/Floors125

9.7.3 Auto-and Chooser-Digitals125

9.7.4 Numerical Implementation125

9.8 Swap Example：Bermudan Swaptions127

9.8.1 Early Notification127

9.8.2 Comparison Between Models128

10．An Empirical Comparison of Market Models131

10.1 Data Description132

10.2 LIBOR Market Model132

10.2.1 Calibration Methodology132

10.2.2 Estimation and Pricing Results134

10.3 Swap Market Model135

10.3.1 Calibration Methodology135

10.3.2 Estimation and Pricing Results135

10.4 Conclusion136

11．Convexity Correction139

11.1 Convexity Correction and Change of Numeraire140

11.1.1 Multi-Currency Change of Numeraire Theorem140

11.1.2 Convexity Correction142

11.2 Options on Convexity Corrected Rates145

11.2.1 Option Price Formula146

11.2.2 Digital Price Formula147

11.3 Single Index Products147

11.3.1 LIBOR in Arrears147

11.3.2 Constant Maturity Swap149

11.3.3 Diffed LIBOR150

11.3.4 Diffed CMS150

11.4 Multi-Index Products151

11.4.1 Rate Based Spread Options151

11.4.2 Spread Digital153

11.4.3 Other Multi-Index Products153

11.4.4 Comparison with Market Models154

11.5 A Warning on Convexity Correction155

11.6 Appendix：Linear Swap Rate Model156

12．Extensions and Further Developments159

12.1 General Philosophy159

12.2 Multi-Factor Models160

12.3 Volatility Skews161

References163

Index167