Calibration and Filtering of Exponential Lévy Option Pricing Models

A well-studied topic in finance is fitting pricing models to available market information; this is the inverse of the option pricing problem. The accuracy of least squares calibration using option premiums and particle filtering of price data to find model parameters is determined. Derivative models using exponential Lévy processes are calibrated using regularized weighted least squares with respect to the minimal entropy martingale measure. Sequential importance resampling is used for the Bayesian inference problem of time series parameter estimation with proposal distribution determined using extended Kalman filter and sample impoverishment is avoided with MCMC. The algorithms converge to their respective global optimums using a statistical optimization approach. Each of these methods follows a complementary path toward achieving the same goal: efficiently calibrate the model of choice to available information. Thus, they should agree on optimal parameters. We investigate this assertion. Math Department University of California, San Diego