Forward-Backward SDEs driven by L\'evy Processes and Application to Option Pricing

Abstract

Recent developments on financial markets have revealed the limits of Brownian motion pricing models when they are applied to actual markets. L\'evy processes, that admit jumps over time, have been found more useful for applications. Thus, we suggest a L\'evy model based on Forward-Backward Stochastic Differential Equations (FBSDEs) for option pricing in a L\'evy-type market. We show the existence and uniqueness of a solution to FBSDEs driven by a L\'evy process. This result is important from the mathematical point of view, and also, provides a much more realistic approach to option pricing.