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Time-Changed Levy Processes and Option Pricing

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Author Info
Peter Carr (New York University)
Liuren Wu (Fordham University)

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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.

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File URL: http://129.3.20.41/eps/fin/papers/0207/0207011.pdf
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Publisher Info
Paper provided by EconWPA in its series Finance with number 0207011.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Length: 42 pages
Date of creation: 30 Aug 2002
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Handle: RePEc:wpa:wuwpfi:0207011

Note: Type of Document - pdf; prepared on MikTex; to print on postscript; pages: 42 ; figures: none. produced via dvipdfm
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Web page: http://129.3.20.41

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Related research
Keywords: random time change; Levy processes; characteristic functions; option pricing; exponen­tial martingales; measure change;

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Find related papers by JEL classification:
G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

References listed on IDEAS
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  1. Markus Leippold & Liuren Wu, 2002. "Asset Pricing Under The Quadratic Class," Finance 0207015, EconWPA. [Downloadable!]
    Other versions:
  2. Rosenberg, Joshua V. & Engle, Robert F., 2002. "Empirical pricing kernels," Journal of Financial Economics, Elsevier, vol. 64(3), pages 341-372, June. [Downloadable!] (restricted)
    Other versions:
  3. Peter Carr & Liuren Wu, 2002. "The Finite Moment Log Stable Process and Option Pricing," Finance 0207012, EconWPA. [Downloadable!]
    Other versions:
  4. Damir Filipovic, 2001. "A general characterization of one factor affine term structure models," Finance and Stochastics, Springer, vol. 5(3), pages 389-412. [Downloadable!] (restricted)
  5. John Y. Campbell & Ludger Hentschel, 1991. "No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns," NBER Working Papers 3742, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  6. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal Of The Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241. [Downloadable!] (restricted)
  7. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 9(1), pages 69-107. [Downloadable!] (restricted)
  8. Torben G. Andersen & Luca Benzoni & Jesper Lund, 2002. "An Empirical Investigation of Continuous-Time Equity Return Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1239-1284, 06. [Downloadable!] (restricted)
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  9. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March. [Downloadable!] (restricted)
  10. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April. [Downloadable!]
  11. Benninga, Simon & Björk, Tomas & Wiener, Zvi, 2002. "On the Use of Numeraires in Option pricing," Working Paper Series in Economics and Finance 484, Stockholm School of Economics. [Downloadable!]
  12. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144. [Downloadable!] (restricted)
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  13. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January. [Downloadable!] (restricted)
  14. 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. [Downloadable!] (restricted)
  15. Frank Milne & Dilip Madan, 1991. "Option Pricing With V. G. Martingale Components," Working Papers 1159, Queen's University, Department of Economics. [Downloadable!]
  16. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-86, March. [Downloadable!] (restricted)
  17. Campbell, J.Y. & Kyle, A.S., 1988. "Smart Money, Noise Trading And Stock Price Behavior," Papers 95, Princeton, Department of Economics - Financial Research Center.
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  18. Ole E. Barndorff-Nielsen, 1997. "Processes of normal inverse Gaussian type," Finance and Stochastics, Springer, vol. 2(1), pages 41-68. [Downloadable!] (restricted)
  19. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238. [Downloadable!] (restricted)
  20. Geert Bekaert & Guojun Wu, 1997. "Asymmetric Volatility and Risk in Equity Markets," NBER Working Papers 6022, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  21. Haugen, Robert A & Talmor, Eli & Torous, Walter N, 1991. " The Effect of Volatility Changes on the Level of Stock Prices and Subsequent Expected Returns," Journal of Finance, American Finance Association, vol. 46(3), pages 985-1007, July. [Downloadable!] (restricted)
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