An Elementary Intoduction to Mathematical Finance:Options and Other Topics2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

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1 Probability1

1.1 Probabilities and Events1

1.2 Conditional Probability5

1.3 Random Variables and Expected Values9

1.4 Covariance and Correlation13

1.5 Exercises15

2 Normal Random Variables20

2.1 Continuous Random Variables20

2.2 Normal Random Variables20

2.3 Properties of Normal Random Variables24

2.4 The Central Limit Theorem27

2.5 Exercises29

3 Geometric Brownian Motion32

3.1 Geometric Brownian Motion32

3.2 Geometric Brownian Motion as a Limit of Simpler Models33

3.3 Brownian Motion35

3.4 Exercises36

4 Interest Rates and Present Value Analysis38

4.1 Interest Rates38

4.2 Present Value Analysis42

4.3 Rate of Return52

4.4 Continuously Varying Interest Rates55

4.5 Exercises57

5 Pricing Contracts via Arbitrage63

5.1 An Example in Options Pricing63

5.2 Other Examples of Pricing via Arbitrage67

5.3 Exercises76

6 The Arbitrage Theorem81

6.1 The Arbitrage Theorem81

6.2 The Multiperiod Binomial Model85

6.3 Proof of the Arbitrage Theorem87

6.4 Exercises91

7 The Black-Scholes Formula95

7.1 Introduction95

7.2 The Black-Scholes Formula95

7.3 Properties of the Black-Scholes Option Cost99

7.4 The Delta Hedging Arbitrage Strategy102

7.5 Some Derivations108

7.5.1 The Black-Scholes Formula108

7.5.2 The Partial Derivatives110

7.6 Exercises115

8 Additional Results on Options118

8.1 Introduction118

8.2 Call Options on Dividend-Paying Securities118

8.2.1 The Dividend for Each Share of the Security Is Paid Continuously in Time at a Rate Equal to a Fixed Fraction f of the Price of the Security119

8.2.2 For Each Share Owned， a Single Payment of fS（td） Is Made at Time td120

8.2.3 For Each Share Owned， a Fixed Amount D Is to Be Paid at Time td121

8.3 Pricing American Put Options123

8.4 Adding Jumps to Geometric Brownian Motion129

8.4.1 When the Jump Distribution Is Lognormal131

8.4.2 When the Jump Distribution Is General133

8.5 Estimating the Volatility Parameter135

8.5.1 Estimating a Population Mean and Variance136

8.5.2 The Standard Estimator of Volatility137

8.5.3 Using Opening and Closing Data139

8.5.4 Using Opening， Closing， and High-Low Data140

8.6 Some Comments142

8.6.1 When the Option Cost Differs from the Black-Scholes Formula142

8.6.2 When the Interest Rate Changes143

8.6.3 Final Comments143

8.7 Appendix145

8.8 Exercises146

9 Valuing by Expected Utility152

9.1 Limitations of Arbitrage Pricing152

9.2 Valuing Investments by Expected Utility153

9.3 The Portfolio Selection Problem160

9.3.1 Estimating Covariances169

9.4 Value at Risk and Conditional Value at Risk170

9.5 The Capital Assets Pricing Model172

9.6 Mean Variance Analysis of Risk-Neutral-Priced Call Options173

9.7 Rates of Return： Single-Period and Geometric Brownian Motion176

9.8 Exercises177

10 Optimization Models181

10.1 Introduction181

10.2 A Deterministic Optimization Model181

10.2.1 A General Solution Technique Based on Dynamic Programming182

10.2.2 A Solution Technique for Concave Return Functions184

10.2.3 The Knapsack Problem188

10.3 Probabilistic Optimization Problems190

10.3.1 A Gambling Model with Unknown Win Probabilities190

10.3.2 An Investment Allocation Model191

10.4 Exercises193

11 Exotic Options196

11.1 Introduction196

11.2 Barrier Options196

11.3 Asian and Lookback Options197

11.4 Monte Carlo Simulation198

11.5 Pricing Exotic Options by Simulation199

11.6 More Efficient Simulation Estimators201

11.6.1 Control and Antithetic Variables in the Simulation of Asian and Lookback Option Valuations201

11.6.2 Combining Conditional Expectation and Importance Sampling in the Simulation of Barrier Option Valuations205

11.7 Options with Nonlinear Payoffs207

11.8 Pricing Approximations via Multiperiod Binomial Models208

11.9 Exercises210

12 Beyond Geometric Brownian Motion Models213

12.1 Introduction213

12.2 Crude Oil Data214

12.3 Models for the Crude Oil Data220

12.4 Final Comments222

13 Autogressive Models and Mean Reversion233

13.1 The Autoregressive Model233

13.2 Valuing Options by Their Expected Return234

13.3 Mean Reversion237

13.4 Exercises239

Index251