CRIF Working Paper No. 02007

Time-Changed Lévy Process and Option Pricing

Title: Time-Changed Lévy Processes and Option Pricing

Authors: Peter Carr (New York University)

             Liuren Wu (Fordham University)

Contact: wu@fordham.edu

Keywords: random time change, Lévy processes, characteristic functions, option pricing, exponential martingales, measure change.

JEL Classification: G10, G12, G13

Abstract: As is well known, the classic Black-Scholes option pricing model assumes that returns follow Brownian motion. It is widely recognized that return processes differ from this benchmark in at least three important ways. First, asset prices jump, leading to non-normal return innovations. Second, return volatilities vary stochastically over time. Third, returns and their volatilities are correlated, often negatively for equities. We propose that time-changed Lévy processes be used to simultaneously address these three facets of the underlying asset return process. We show that our framework encompasses almost all of the models proposed in the option pricing literature. Despite the generality of our approach, we show that it is straightforward to select and test a particular option pricing model through the use of characteristic function technology.

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Comments: The paper is forthcoming in Journal of Financial Economics.