Time-Changed Levy Process and Option Pricing
35 Pages Posted: 26 Sep 2001
Date Written: September 20, 2001
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
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