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

TL;DR

This paper introduces a Le9vy process-based model using Forward-Backward Stochastic Differential Equations for more realistic option pricing in markets with jumps, addressing limitations of traditional Brownian motion models.

Contribution

It establishes the existence and uniqueness of solutions to FBSDEs driven by Le9vy processes, enhancing mathematical understanding and practical application in finance.

Findings

Proves existence and uniqueness of solutions to Le9vy-driven FBSDEs.

Demonstrates the model's realism for option pricing.

Provides a mathematically rigorous framework for jump market models.

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.