A Simple Calibration Procedure of Stochastic Volatility Models with Jumps by Short Term Asymptotics

In this paper we propose a simple non-parametric calibration procedure of option prices based on the short term asymptotics of implied volatilities. The approximation formula is derived for a general one factor jump-diffusion specification nesting most of the theoretical models typically used for option pricing. Using sets of reasonable parameter values we show that the procedure is capable of producing accurate estimates of key model functional relationships. Its implementation on a set of S&P500 option price data yields two major empirical results. First, the square root process for the variance is not consistent with the data. Second, Poisson jumps in returns do not help explaining the skew of short term implied volatilities.