An Undergraduate Introduction to Financial Mathematics 4th Edition by Robert Buchanan ISBN 9789811260308 9811260303

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ISBN 10: 9811260303
ISBN 13: 9789811260308
Author: Robert Buchanan

Anyone with an interest in learning about the mathematical modeling of prices of financial derivatives such as bonds, futures, and options can start with this book, whereby the only mathematical prerequisite is multivariable calculus. The necessary theory of interest, statistical, stochastic, and differential equations are developed in their respective chapters, with the goal of making this introductory text as self-contained as possible.

In this edition, the chapters on hedging portfolios and extensions of the Black–Scholes model have been expanded. The chapter on optimizing portfolios has been completely re-written to focus on the development of the Capital Asset Pricing Model. The binomial model due to Cox–Ross–Rubinstein has been enlarged into a standalone chapter illustrating the wide-ranging utility of the binomial model for numerically estimating option prices. There is a completely new chapter on the pricing of exotic options. The appendix now features linear algebra with sufficient background material to support a more rigorous development of the Arbitrage Theorem.

The new edition has more than doubled the number of exercises compared to the previous edition and now contains over 700 exercises. Thus, students completing the book will gain a deeper understanding of the development of modern financial mathematics.

An Undergraduate Introduction to Financial Mathematics 4th Edition Table of contents:

1. The Theory of Interest

1.1 Simple Interest

1.2 Compound Interest

1.3 Continuously Compounded Interest

1.4 Present Value

1.5 Rate of Return

1.6 Time-Varying Interest Rates

1.7 Continuous Income Streams

2. Discrete Probability

2.1 Events and Probabilities

2.2 Random Variables

2.3 Addition Rule

2.4 Conditional Probability and Multiplication Rule

2.5 Cumulative Distribution Functions

2.6 Binomial Random Variables

2.7 Expected Value

2.8 Variance and Standard Deviation

2.9 Covariance and Correlation

2.10 Odds and Wagering

3. The Arbitrage Theorem

3.1 An Introduction to Linear Programming

3.2 Primal and Dual Problems

3.3 The Fundamental Theorem of Finance

3.4 Remarks

4. Optimal Portfolio Choice

4.1 Return and Risk

4.2 The Efficient Frontier

4.3 The Capital Asset Pricing Model

4.4 Uncorrelated Returns

4.5 Utility Functions

5. Forwards and Futures

5.1 Definition of a Forward Contract

5.2 Pricing a Forward Contract

5.3 Dividends and Pricing

5.4 Incorporating Transaction and Storage Costs

5.5 Synthetic Forwards

5.6 Futures

6. Options

6.1 Properties of Options

6.2 Including the Effects of Dividends

6.3 Parity and American Options

6.4 Option Strategies

7. Approximating Option Prices Using Binomial Trees

7.1 One Period Binomial Model

7.2 Multi-Period Binomial Models

7.3 Estimating Increase/Decrease Factors

7.4 American Options

8. Normal Random Variables and Probability

8.1 Continuous Random Variables

8.2 Expected Value of Continuous Random Variables

8.3 Variance and Standard Deviation

8.4 Normal Random Variables

8.5 Lognormal Random Variables

8.6 Application: Portfolio Selection with Utility

8.7 Partial Expectation

8.8 The Binormal Distribution

9. Random Walks and Brownian Motion

9.1 Empirical Justification for the Mathematical Model

9.2 Advection/Diffusion Equation

9.3 Continuous Random Walk

9.4 The Stochastic Integral

9.5 Itô’s Lemma

9.6 Maximum and Minimum of a Random Walk

10. Black–Scholes Equation and Option Formulas

10.1 Black–Scholes Partial Differential Equation

10.2 Boundary and Initial Conditions

10.3 Changing Variables in the Black–Scholes PDE

10.4 Solving the Black–Scholes Equation

10.5 Derivation Using the Binomial Model

11. Extensions of the Black–Scholes Model

11.1 Options on Exchange Rates

11.2 Options on Futures

11.3 Options on Stocks Paying Discrete Dividends

12. Derivatives of Black–Scholes Option Prices

12.1 Delta and Gamma

12.2 Theta

12.3 Vega, Rho, and Psi

12.4 Applications of the Greeks

13. Hedging

13.1 General Principles

13.2 Delta Hedging

13.3 Self-Financing Portfolios

13.4 Gamma-Neutral Portfolios

14. Exotic Options

14.1 Gap Options

14.2 Power Options

14.3 Exchange Options

14.4 Chooser Options

14.5 Forward Start Options

14.6 Compound Options

14.7 Asian Options

14.8 Barrier Options

Appendix A Linear Algebra Primer

A.1 Matrices and their Properties

A.2 Vector and Matrix Norms

A.3 Separating Hyperplanes and Convex Cones

A.4 Farkas’ Lemma

Bibliography

Index

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