Time-Changed Levy Processes and Option Pricing

Peter Carr and Liuren Wu ()
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Peter Carr: New York University

Finance from EconWPA

Abstract: As is well known, the classic Black­Scholes 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 non­normal return innovations. Second, return volatilities vary stochastically over time. Third, returns and their volatilities are correlated, often negatively for equities. We propose that time­changed Levy 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.

Keywords: random time change; Levy processes; characteristic functions; option pricing; exponen­tial martingales; measure change (search for similar items in EconPapers)
JEL-codes: G10 G12 G13 (search for similar items in EconPapers)
Date: 2002-08-30
Note: Type of Document - pdf; prepared on MikTex; to print on postscript; pages: 42 ; figures: none. produced via dvipdfm
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Journal Article: Time-changed Levy processes and option pricing (2004)
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Persistent link: http://EconPapers.repec.org/RePEc:wpa:wuwpfi:0207011

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