Pricing Path-Dependent Options with Discrete Monitoring Under Time-Changed Levy Processes

Abstract

This paper proposes a pricing method for path-dependent derivatives with discrete monitoring when an underlying asset price is driven by a time-changed Levy process. The key to our method is to derive a backward recurrence relation for computing the multivariate characteristic functions of the intertemporal joint distribution of time-changed Levy processes. Using the derived representation of the characteristic function we obtain semi-analytical pricing formulas for geometric Asian, forward start, barrier, fader, and lookback options, all of which are discretely monitored.

Keywords: time-changed Levy process, intertemporal joint distribution, multivariate characteristic function, Fourier transform, path-dependent options

JEL Classification: G13, C63