Undergraduate Introduction to Financial Mathematicsn (2nd Edition) / Edition 2

ISBN-10: 9812835350

ISBN-13: 9789812835352

Pub. Date: 12/25/2008

Publisher: World Scientific Publishing Company, Incorporated

This textbook provides an introduction to financial mathematics and financial engineering for undergraduate students who have completed a three- or four-semester sequence of calculus courses.It introduces the Theory of Interest, discrete and continuous random variables and probability, stochastic processes, linear programming, the Fundamental Theorem of Finance,

Overview

This textbook provides an introduction to financial mathematics and financial engineering for undergraduate students who have completed a three- or four-semester sequence of calculus courses.It introduces the Theory of Interest, discrete and continuous random variables and probability, stochastic processes, linear programming, the Fundamental Theorem of Finance, option pricing, hedging, and portfolio optimization. The reader progresses from a solid grounding in multi-variable calculus through a derivation of the Black-Scholes equation, its solution, properties, and applications.

Product Details

ISBN-13:
9789812835352
Publisher:
World Scientific Publishing Company, Incorporated
Publication date:
12/25/2008
Edition description:
Older Edition
Pages:
372
Product dimensions:
6.10(w) x 9.10(h) x 1.00(d)

Related Subjects

Preface vii

Preface to the First Edition ix

1 The Theory of Interest 1

1.1 Simple Interest 1

1.2 Compound Interest 3

1.3 Continuously Compounded Interest 4

1.4 Present Value 6

1.5 Rate of Return 12

1.6 Exercises 13

2 Discrete Probability 17

2.1 Events and Probabilities 18

2.3 Conditional Probability and Multiplication Rule 20

2.4 Random Variables and Probability Distributions 23

2.5 Binomial Random Variables 25

2.6 Expected Value 26

2.7 Variance and Standard Deviation 32

2.8 Exercises 36

3 Normal Random Variables and Probability 39

3.1 Continuous Random Variables 39

3.2 Expected Value of Continuous Random Variables 42

3.3 Variance and Standard Deviation 45

3.4 Normal Random Variables 46

3.5 Central Limit Theorem 54

3.6 Lognormal Random Variables 57

3.7 Properties of Expected Value 61

3.8 Properties of Variance 64

3.9 Exercises 66

4 The Arbitrage Theorem 71

4.1 The Concept of Arbitrage 71

4.2 Duality Theorem of Linear Programming 73

4.2.1 Dual Problems 78

4.3 The Fundamental Theorem of Finance 86

4.4 Exercises 88

5 Random Walks and Brownian Motion 91

5.1 Intuitive Idea of a Random Walk 91

5.2 First Step Analysis 92

5.3 Intuitive Idea of a Stochastic Process 105

5.4 Ito Processes 115

5.5 Ito's Lemma 116

5.6 Stock Market Example 118

5.7 Exercises 121

6 Forwards and Futures 123

6.1 Definition of a Forward Contract 123

6.2 Pricing a Forward Contract 125

6.3 Dividends and Pricing 130

6.4 Incorporating Transaction Costs 131

6.5 Futures 133

6.6 Exercises 136

7 Options 139

7.1 Properties of Options 140

7.2 Pricing an Option Using a Binary Model 143

7.3 Black-Scholes PartialDifferential Equation 146

7.4 Boundary and Initial Conditions 148

7.5 Exercises 150

8 Solution of the Black-Scholes Equation 153

8.1 Fourier Transforms 153

8.2 Inverse Fourier Transforms 156

8.3 Changing Variables in the Black-Scholes PDE 158

8.4 Solving the Black-Scholes Equation 161

8.5 Binomial Model (Optional) 165

8.6 Exercises 177

9 Derivatives of Black-Scholes Option Prices 181

9.1 Theta 181

9.2 Delta 183

9.3 Gamma 185

9.4 Vega 186

9.5 Rho 188

9.6 Relationships Between Δ, Θ, and t 189

9.7 Exercises 191

10 Hedging 193

10.1 General Principles 193

10.2 Delta Hedging 196

10.3 Delta Neutral Portfolios 201

10.4 Gamma Neutral Portfolios 202

10.5 Exercises 204

11 Optimizing Portfolios 207

11.1 Covariance and Correlation 207

11.2 Optimal Portfolios 215

11.3 Utility Functions 218

11.4 Expected Utility 224

11.5 Portfolio Selection 226

11.6 Minimum Variance Analysis 230

11.7 Mean-Variance Analysis 241

11.8 Exercises 246

12 American Options 251

12.1 Parity and American Options 251

12.2 American Puts Valued by a Binomial Model 255

12.3 Properties of the Binomial Pricing Formula 261

12.4 Optimal Exercise Time 266

12.5 Exercises 269

Appendix A Sample Stock Market Data 273

Appendix B Solutions to Chapter Exercises 277

B.1 The Theory of Interest 277

B.2 Discrete Probability 280

B.3 Normal Random Variables and Probability 286

B.4 The Arbitrage Theorem 298

B.5 Random Walks and Brownian Motion 305

B.6 Forwards and Futures 311

B.7 Options 313

B.8 Solution of the Black-Scholes Equation 316

B.9 Derivatives of Black-Scholes Option Prices 324

B.10 Hedging 327

B.11 Optimizing Portfolios 332

B.12 American Options 343

Bibliography 347

Index 351

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