金融数学 英文版2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

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1.Financial Markets1

1.1 Markets and Math1

1.2 Stocks and Their Derivatives2

1.2.1 Forward Stock Contracts3

1.2.2 Call Options7

1.2.3 Put Options9

1.2.4 Short Selling11

1.3 Pricing Futures Contracts12

1.4 Bond Markets15

1.4.1 Rates of Return16

1.4.2 The U.S.Bond Market17

1.4.3 Interest Rates and Forward Interest Rates18

1.4.4 Yield Curves19

1.5 Interest Rate Futures20

1.5.1 Determining the Futures Price20

1.5.2 Treasury Bill Futures21

1.6 Foreign Exchange22

1.6.1 Currency Hedging22

1.6.2 Computing Currency Futures23

2."Binomial Trees,Replicating Portfolios,and Arbitrage"25

2.1 Three Ways to Price a Derivative25

2.2 The Game Theory Method26

2.2.1 Eliminating Uncertainty27

2.2.2 Valuing the Option27

2.2.3 Arbitrage27

2.2.4 The Game Theory Method—A General Formula28

2.3 Replicating Portfolios29

2.3.1 The Context30

2.3.2 A Portfolio Match30

2.3.3 Expected Value Pricing Approach31

2.3.4 How to Remember the Pricing Probability32

2.4 The Probabilistic Approach34

2.5 Risk36

2.6 Repeated Binomial Trees and Arbitrage39

2.7 Appendix:Limits of the Arbitrage Method41

3.Tree Models for Stocks and Options44

3.1 A Stock Model44

3.1.1 Recombining Trees46

3.1.2 Chaining and Expected Values46

3.2 Pricing a Call Option with the Tree Model49

3.3 Pricing an American Option52

3.4 Pricing an Exotic Option—Knockout Options55

3.5 Pricing an Exotic Option—Lookback Options59

3.6 Adjusting the Binomial Tree Model to Real-World Data61

3.7 Hedging and Pricing the N-Period Binomial Model66

4.Using Spreadsheets to Compute Stock and Option Trees71

4.1 Some Spreadsheet Basics71

4.2 Computing European Option Trees74

4.3 Computing American Option Trees77

4.4 Computing a Barrier Option Tree79

4.5 Computing N-Step Trees80

5.Continuous Models and the Black-Scholes Formula81

5.1 A Continuous-Time Stock Model81

5.2 The Discrete Model82

5.3 An Analysis of the Continuous Model87

5.4 The Black-Scholes Formula90

5.5 Derivation of the Black-Scholes Formula92

5.5.1 The Related Model92

5.5.2 The Expected Value94

5.5.3 Two Integrals94

5.5.4 Putting the Pieces Together96

5.6 Put-Call Parity97

5.7 Trees and Continuous Models98

5.7.1 Binomial Probabilities98

5.7.2 Approximation with Large Trees100

5.7.3 Scaling a Tree to Match a GBM Model102

5.8 The GBM Stock Price Model-A Cautionary Tale103

5.9 Appendix:Construction of a Brownian Path106

6.The Analytic Approach to Black-Scholes109

6.1 Strategy for Obtaining the Differential Equation110

6."2 Expanding V(S,t)110

6."3 Expanding and Simplifying V(St,t)111

6.4 Finding a Portfolio112

6.5 Solving the Black-Scholes Differential Equation114

6.5.1 Cash or Nothing Option114

6.5.2 Stock-or-Nothing Option115

6.5.3 European Call116

6.6 Options on Futures116

6.6.1 Call on a Futures Contract117

6.6.2 A PDE for Options on Futures118

6.7 Appendix:Portfolio Differentials120

7.Hedging122

7.1 Delta Hedging122

7."1.1 Hedging,Dynamic Programming,and a Proof that Black-Scholes Really Works in an Idealized World123

7.1.2 Why the Foregoing Argument Does Not Hold in the Real World124

7.1.3 Earlier △ Hedges125

7.2 Methods for Hedging a Stock or Portfolio126

7.2.1 Hedging with Puts126

7.2.2 Hedging with Collars127

7.2.3 Hedging with Paired Trades127

7.2.4 Correlation-Based Hedges127

7.2.5 Hedging in the Real World128

7.3 Implied Volatility128

7.3.1 Computing ？ with Maple128

7.3.2 The Volatility Smile129

7."4 The Parameters△,Г,and Θ130

7.4.1 The Role of Г131

7."4.2 A Further Role for △,Г,Θ133

7.5 Derivation of the Delta Hedging Rule134

7.6 Delta Hedging a Stock Purchase135

8.Bond Models and Interest Rate Options137

8.1 Interest Rates and Forward Rates137

8.1.1 Size138

8.1.2 The Yield Curve138

8.1.3 How Is the Yield Curve Determined?139

8.1.4 Forward Rates139

8.2 Zero-Coupon Bonds140

8.2.1 Forward Rates and ZCBs140

8.2.2 Computations Based on Y(t) or P(t)142

8.3 Swaps144

8.3.1 Another Variation on Payments147

8.3.2 A More Realistic Scenario148

8.3.3 Models for Bond Prices149

8.3.4 Arbitrage150

8.4 Pricing and Hedging a Swap152

8.4.1 Arithmetic Interest Rates153

8.4.2 Geometric Interest Rates155

8.5 Interest Rate Models157

8.5.1 Discrete Interest Rate Models158

8.5.2 Pricing ZCBs from the Interest Rate Model162

8.5.3 The Bond Price Paradox165

8.5.4 Can the Expected Value Pricing Method Be Arbitraged?166

8.5.5 Continuous Models171

8.5.6 A Bond Price Model171

8.5.7 A Simple Example174

8.5.8 The Vasicek Model178

8.6 Bond Price Dynamics180

8.7 A Bond Price Formula181

8."8 Bond Prices,Spot Rates,and HJM183

8.8.1 Example:The Hall-White Model184

8.9 The Derivative Approach to HJM:The HJM Miracle186

8.10 Appendix:Forward Rate Drift188

9.Computational Methods for Bonds190

9.1 Tree Models for Bond Prices190

9.1.1 Fair and Unfair Games190

9.1.2 The Ho-Lee Model192

9.2 A Binomial Vasicek Model:A Mean Reversion Model200

9.2.1 The Base Case201

9.2.2 The General Induction Step202

10.Currency Markets and Foreign Exchange Risks207

10.1 The Mechanics of Trading207

10.2 Currency Forwards:Interest Rate Parity209

10.3 Foreign Currency Options211

10.3.1 The Garman-Kohlhagen Formula211

10.3.2 Put-Call Parity for Currency Options213

10.4 Guaranteed Exchange Rates and Quantos214

10.4.1 The Bond Hedge215

10.4.2 Pricing the GER Forward on a Stock216

10.4.3 Pricing the GER Put or Call Option219

10.5 To Hedge or Not to Hedge—and How Much220

11.International Political Risk Analysis221

11.1 Introduction221

11.2 Types of International Risks222

11.2.1 Political Risk222

11.2.2 Managing International Risk223

11.2.3 Diversification223

11.2.4 Political Risk and Export Credit Insurance224

11.3 Credit Derivatives and the Management of Political Risk225

11.3.1 Foreign Currency and Derivatives225

11.3.2 Credit Default Risk and Derivatives226

11.4 Pricing International Political Risk228

11.4.1 The Credit Spread or Risk Premium on Bonds229

11.5 Two Models for Determining the Risk Premium230

11.5.1 The Black-Scholes Approach to Pricing Risky Debt230

11.5.2 An Alternative Approach to Pricing Risky Debt234

11.6 A Hypothetical Example of the JLT Model238