Pricing Path-Dependent Options with Discrete Monitoring under Time-Changed Lévy Processes

Yuji Umezawa and Akira Yamazaki

Applied Mathematical Finance, 2015, vol. 22, issue 2, 133-161

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.

Date: 2015
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DOI: 10.1080/1350486X.2014.960529

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