Higham D. An Introduction to Financial Option Valuation Mathematics,..Comp. 2004

Textbook in PDF format

This is a lively textbook providing a solid introduction to financial option valuation for undergraduate students armed with a working knowledge of a first year calculus. Written in a series of short chapters, its self-contained treatment gives equal weight to applied mathematics, stochastics and computational algorithms. No prior background in probability, statistics or numerical analysis is required. Detailed derivations of both the basic asset price model and the Black–Scholes equation are provided along with a presentation of appropriate computational techniques including binomial, finite differences and in particular, variance reduction techniques for the Monte Carlo method. Each chapter comes complete with accompanying stand-alone MatLAB code listing to illustrate a key idea. Furthermore, the author has made heavy use of figures and examples, and has included computations based on real stock market data.
Options
Option Valuation Preliminaries
Random Variables
Computer Simulation
Asset price movement
Asset price model: part I
Asset price model: part II
Black--Scholes PDE and Formulas
More on hedging
The Greeks
More on the Black-Scholes Formulas
Risk neutrality
Solving a nonlinear equation
Implied volatility
Monte Carlo method
Binomial method
Cash-or-nothing options
American options
Exotic options
Historical volatility
Monte Carlo part II: variance reduction by antithetic variates
Monte Carlo part III: variance reduction by control variates
Finite difference methods
Finite difference methods for the Black-Scholes PDE