Stochastic Financial Models

This monograph presents a novel numerical approach to solving partial integro-differential equations arising in asset pricing models with jumps, which greatly exceeds the efficiency of existing approaches.

This book is an extension of “Probability for Finance” to multi-period financial models, either in the discrete or continuous-time framework. It describes the most important stochastic processes used in finance in a pedagogical way, especially Markov chains, Brownian motion and martingales. It also shows how mathematical tools like filtrations, Itô’s lemma or Girsanov theorem should be understood in the framework of financial models. It also provides many illustrations coming from the financial literature.

This book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes.