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

27 Pages Posted: 11 Sep 2012 Last revised: 17 Sep 2014

Yuji Umezawa

Mizuho-DL Financial Technology Co., Ltd.

Akira Yamazaki

Hosei University - Graduate School of Business Administration

Date Written: April 2, 2014

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

Suggested Citation

Umezawa, Yuji and Yamazaki, Akira, Pricing Path-Dependent Options with Discrete Monitoring Under Time-Changed Levy Processes (April 2, 2014). Applied Mathematical Finance, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2144304 or http://dx.doi.org/10.2139/ssrn.2144304

Yuji Umezawa

Mizuho-DL Financial Technology Co., Ltd. ( email )

Japan

Akira Yamazaki (Contact Author)

Hosei University - Graduate School of Business Administration ( email )

Japan

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