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.