On Sequential Calibration for an Asset Price Model with Piecewise Lévy Processes

We propose simple sequential calibration for an asset price model driven by piecewise Lévy processes, for which simulation methods and Greeks formulas are available. The proposed methods are easy to implement and consist of fitting a sequence of Lévy processes to a return series such that they allow parameters to change at discrete points in time, so that the fitted process can be made consistent with option prices with a range of maturity dates. Given a sequence of implied characteristic functions obtained from quants calibration routine, three calibration criteria are discussed; calibration to implied probability densities, to implied option premiums, and directly to the market quotes. Numerical results on equity index volatilities indicates that without calibrating to market quotes through the Fourier inversion, our method achieves a sufficient calibration accuracy with significantly lighter computation load.