Willmot P. The Mathematics of Financial Derivatives: A Student Introduction

Part I. Basic Option Theory: An introduction to options and markets.
Asset price random walks.
The Black-Scholes model.
Partial differential equations.
The Black–Scholes formulae.
Variations on the Black-Scholes model.
American options.
Part II. Numerical Methods: Finite-difference methods.
Methods for American options.
Binomial methods.
Part III. Further Option Theory: Exotic and path-dependent options.
Barrier options.
A unifying framework for path-dependent options.
Asian options.
Lookback options.
Options with transaction costs.
Part IV. Interest Rate Derivative Products: Interest rate derivatives.
Convertible bonds.
Hints to selected exercises.
Bibliography.
Index.