Stochastic Calculus and Finance

Stochastic Calculus for Finance evolved from the first ten years of the Carnegie Mellon Professional Master program in Computational Finance. The content of this book has been used successfully with students whose mathematics background consists of calculus and calculus-based probability.

The book gives both precise statements of results, plausibility arguments, and even some proofs, but more importantly intuitive explanations developed and refine through classroom experience with this material are provided. The book includes a self-contained treatment of the probability theory needed for stochastic calculus, including Brownian motion and its properties. Advanced topics include foreign exchange models, forward measures, and jump-diffusion processes.

This book is being published in two volumes. The first volume presents the binomial asset-pricing model primarily as a vehicle for introducing in the simple setting the concepts needed for the continuous-time theory in the second volume.