A Simple Option Formula for General Jump-Diffusion and Other Exponential Levy Processes

Option values are well-known to be the integral of a discounted transition density times a payofffunction; this is just martingale pricing. It's usually done in "S-space", where S is the terminalsecurity price. But, for L6vy processes the S-space transition densities are often verycomplicated, involving many special functions and infinite summations. Instead, we show thatit's much easier to compute the option value as an integral in Fourier space - and interpret this asa Parseval identity. ...