Pricing Path-Dependent Options with Discrete Monitoring Under Time-Changed Levy Processes
27 Pages Posted: 11 Sep 2012 Last revised: 17 Sep 2014
Date Written: April 2, 2014
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
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