Time-Changed Levy Process and Option Pricing

35 Pages Posted: 26 Sep 2001

See all articles by Peter Carr

Peter Carr

New York University Finance and Risk Engineering

Liuren Wu

City University of New York, CUNY Baruch College - Zicklin School of Business

Date Written: September 20, 2001

Abstract

We apply stochastic time change to Levy processes to generate a wide variety of tractable option pricing models. In particular, we prove a fundamental theorem that transforms the characteristic function of the time-changed Levy process into the Laplace transform of the stochastic time under appropriate measure change. We extend the traditional measure theory into the complex domain and define the measure change by a class of complex valued exponential martingales. We provide extensive examples to illustrate its applications and its link to existing models in the literature.

Keywords: Stochastic time change, Levy processes, subordination, characteristic functions, option pricing, exponential martingales, measure change.

JEL Classification: G10, G12, G13

Suggested Citation

Carr, Peter P. and Wu, Liuren, Time-Changed Levy Process and Option Pricing (September 20, 2001). Available at SSRN: https://ssrn.com/abstract=283999 or http://dx.doi.org/10.2139/ssrn.283999

Peter P. Carr

New York University Finance and Risk Engineering ( email )

6 MetroTech Center
Brooklyn, NY 11201
United States
9176217733 (Phone)

HOME PAGE: http://engineering.nyu.edu/people/peter-paul-carr

Liuren Wu (Contact Author)

City University of New York, CUNY Baruch College - Zicklin School of Business ( email )

One Bernard Baruch Way
Box B10-247
New York, NY 10010
United States
646-312-3509 (Phone)
646-312-3451 (Fax)

HOME PAGE: http://faculty.baruch.cuny.edu/lwu/

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