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 Lévy process. The key to our method is to derive a backward recurrence relation for computing the multivariate characteristic function of the intertemporal joint distribution of the time-changed Lévy process. 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.
Notes
1 We are not concerned with the implementation of numerical algorithms for the multivariate Fourier transform. However, we acknowledge that there are a number of efficient algorithms for computational finance in the existing literature. For example, see Section 5 in Griebsch and Wystup (Citation2011).