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Time-Changed Levy Processes and Option Pricing

  • Peter Carr

    (New York University)

  • Liuren Wu

    (Fordham University)

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.

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Paper provided by EconWPA in its series Finance with number 0207011.

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Length: 42 pages
Date of creation: 30 Aug 2002
Date of revision:
Handle: RePEc:wpa:wuwpfi:0207011
Note: Type of Document - pdf; prepared on MikTex; to print on postscript; pages: 42 ; figures: none. produced via dvipdfm
Contact details of provider: Web page: http://128.118.178.162

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  1. Ole E. Barndorff-Nielsen, 1997. "Processes of normal inverse Gaussian type," Finance and Stochastics, Springer, vol. 2(1), pages 41-68.
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  17. Benninga, Simon & Björk, Tomas & Wiener, Zvi, 2002. "On the Use of Numeraires in Option pricing," SSE/EFI Working Paper Series in Economics and Finance 484, Stockholm School of Economics.
  18. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
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