Intro to computational finance with MatLab

One book which I've used and can heartily recommend is Higham's An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation, published by Cambridge (2004). This book has been written for a leisurely but stimulating one-semester course in computational finance at the undergrad level; the code is in MatLab.

The first thing to commend this book is that little background is assumed either in terms of mathematics or programming. Any American student who has taken three semesters of calculus should be able to follow the book (though it would be helpful if one came with a stronger math and programming background). And the MatLab code to implement the various algorithms is given in full.

The second thing to commend this book is how far it manages to go assuming such a threadbare background: in 24 chapters spanning 270 pages, the author covers, inter alia, Monte Carlo, variance reduction, the Binomial method, the Black-Scholes PDE, hedging, the Greeks, implied volatility, exotic options, and finite difference methods.

Students in MBA programs should also find the book useful and those in MFE programs might want it as a supplementary text (it's too elementary to serve as the main text in an MFE computational math course, for which something like Brandimarte's Numerical Methods in Finance and Economics might be more appropriate).