Saddlepoint approximations to option price in a general equilibrium model (Q2483862)

This paper deals with applications of the saddlepoint approximations to compute the price of European options, where return processes are from a general equilibrium model. The authors show that the saddlepoint approximations methodology is applicable and can be easily implemented under a general equilibrium model, in particular, when the moment generating function or equivalently cumulant generating function of log-price process is known and analytic in some area. The authors develop a jump-diffusion model, calibrate the model on the S\&P 500 index by applying the Lugannani-Rice formula to European call option price. The accuracy of proposed methodology is verified by comparing it with the Fourier inversion and Monte Carlo simulation.