The mathematics of financial derivatives : a student introduction / Paul Wilmott, Sam Howison, Jeff Dewynne.
Saved in:
| Online Access: |
Full Text (via Cambridge) |
|---|---|
| Main Author: | |
| Other Authors: | , |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Oxford ; New York :
Cambridge University Press,
1995.
|
| Subjects: |
Table of Contents:
- Cover; The Mathematics of Financial Derivatives; Dedication; Title; Copyright; Contents; Preface; Further Reading; Exercises; Part one: Basic Option Theory; 1 An Introduction to Options and Markets; 1.1 Introduction; 1.2 What is an Option?; A Simple Example: A Call Option; Put Options; 1.3 Reading the Financial Press; 1.4 What are Options For?; 1.5 Other Types of Option; 1.6 Forward and Futures Contracts; 1.7 Interest Rates and Present Value; Further Reading; Exercises; 2 Asset Price Random Walks; 2.1 Introduction; 2.2 A Simple Model for Asset Prices; 2.3 Itô's Lemma.
- 2.4 The Elimination of RandomnessFurther Reading; Exercises; 3 The Black−Scholes Model; 3.1 Introduction; 3.2 Arbitrage; 3.3 Option Values, Payoffs and Strategies; 3.4 Put-call Parity; 3.5 The Black-Scholes Analysis; 3.6 The Black-Scholes Equation; 3.7 Boundary and Final Conditions for European Options; 3.8 The Black−Scholes Formulre for European Options; 3.9 Hedging in Practice; 3.10 Implied Volatility; Further Reading; Exercises; 4 Partial Differential Equations; 4.1 Introduction; 4.2 The Diffusion Equation; 4.3 Initial and Boundary Conditions
- 4.3.1 The Initial Value Problem on a Finite Interval4.3.2 The Initial Value Problem on an Infinite Interval; 4.4 Forward versus Backward; Further Reading; Exercises; 5 The Black-Scholes Formulre; 5.1 Introduction; 5.2 Similarity Solutions; 5.3 An initial value problem for the diffusion equation; 5.4 The Black-Scholes Formulre Derived; 5.5 Binary Options; 5.6 Risk Neutrality; Further Reading; Exercises; 6 Variations on the Black-Scholes Model; 6.1 Introduction; 6.2 Options on Dividend-paying Assets; 6.2.1 Dividend Structures; 6.2.2 A Constant Dividend Yield; 6.2.3 Discrete Dividend Payments.
- 6.2.4 Jump Conditions for Discrete Dividends6.2.5 The Call Option with One Dividend Payment; 6.3 Forward and Futures Contracts; 6.4 Options on Futures; 6.5 Time-dependent parameters in the Black-Scholes equation; Further Reading; Exercises; 7 American Options; 7.1 Introduction; 7.2 The Obstacle Problem; 7.3 American Options as Free Boundary Problems; 7.4 The American Put; 7.5 Other American Options; 7.6 Linear Complementarity Problems; 7.6.1 The Obstacle Problem; 7.6.2 A Linear Complementarity Problem for the American Put Option; 7.7 The American Call with Dividends.
- 7. 7.1 General Results on American Call Options7.7.2 A Local Analysis of the Free Boundary; Further Reading; Exercises; Part two: Numerical Methods; 8 Finite-difference Methods; 8.1 Introduction; 8.2 Finite-difference Approximations; 8.3 The Finite-difference Mesh; 8.4 The Explicit Finite-difference Method; 8.5 Implicit Finite-difference Methods; 8.6 The Fully-implicit Method; 8.6.1 Practical Considerations; 8.6.2 The LU Method; 8.6.3 The SOR Method; 8.6.4 The Implicit Finite-difference Algorithm; 8.7 The Crank-Nicolson Method; Further Reading; Exercises; 9 Methods for American Options.