Abstract: We employ a jump-diffusion model for asset prices whose assets jump sizes have a weighed average -exponential distribution.Under this model, to study the option pricing, we need to study the first passage time. In this paper the first passage time is derived, and the joint distribution of first passage time and the overshoot and the joint distribution of first passage time and return process are obtained by solving the equation with martingale method. 

Key words: Weighed average index , Jump-diffusion model , Return process, First passage time , The over-shoot, Joint distribution