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Dampened Power Law: Reconciling the Tail Behavior of Financial Security Returns

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Author Info
Liuren Wu (Zicklin School of Business, Baruch College)

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Abstract

This article proposes a stylized model that reconciles several seemingly conflicting findings on financial security returns and option prices. The model is based on a pure jump Lévy process, wherein the jump arrival rate obeys a power law dampened by an exponential function. The model allows for different degrees of dampening for positive and negative jumps and also for different pricing for upside and downside market risks. Calibration of the model to the S&P 500 index shows that the market charges only a moderate premium on upward index movements but the maximally allowable premium on downward index movements.

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File URL: http://www.journals.uchicago.edu/cgi-bin/resolve?JB790314
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Publisher Info
Article provided by University of Chicago Press in its journal Journal of Business.

Volume (Year): 79 (2006)
Issue (Month): 3 (May)
Pages: 1445-1474
Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Handle: RePEc:ucp:jnlbus:v:79:y:2006:i:3:p:1445-1474

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Rosenberg, Joshua V. & Engle, Robert F., 2002. "Empirical pricing kernels," Journal of Financial Economics, Elsevier, vol. 64(3), pages 341-372, June. [Downloadable!] (restricted)
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  2. Peter Carr & Liuren Wu, 2002. "Time-Changed Levy Processes and Option Pricing," Finance 0207011, EconWPA. [Downloadable!]
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  3. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 13(2), pages 433-51.
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  4. David S. Bates, 2001. "The Market for Crash Risk," NBER Working Papers 8557, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  5. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," Journal of Business, University of Chicago Press, vol. 36, pages 394. [Downloadable!]
  6. Albert N. Shiryaev & Jan Kallsen, 2002. "The cumulant process and Esscher's change of measure," Finance and Stochastics, Springer, vol. 6(4), pages 397-428. [Downloadable!] (restricted)
  7. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-778, 04. [Downloadable!] (restricted)
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  8. David Backus & Silverio Foresi & Liuren Wu, 2002. "Accouting for Biases in Black-Scholes," Finance 0207008, EconWPA. [Downloadable!]
  9. Hagerman, Robert L, 1978. "More Evidence on the Distribution of Security Returns," Journal of Finance, American Finance Association, vol. 33(4), pages 1213-21, September. [Downloadable!] (restricted)
  10. Yacine Ait-Sahalia & Andrew W. Lo, 1995. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," NBER Working Papers 5351, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  11. 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!]
  12. Hall, Joyce A. & Brorsen, B. Wade & Irwin, Scott H., 1989. "The Distribution of Futures Prices: A Test of the Stable Paretian and Mixture of Normals Hypotheses," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(01), pages 105-116, March. [Downloadable!]
  13. 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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  14. 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)
  15. 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)
  16. Laurent Calvet & Adlai Fisher, 2002. "Multifractality In Asset Returns: Theory And Evidence," The Review of Economics and Statistics, MIT Press, vol. 84(3), pages 381-406, August. [Downloadable!] (restricted)
  17. Frank Milne & Dilip Madan, 1991. "Option Pricing With V. G. Martingale Components," Working Papers 1159, Queen's University, Department of Economics. [Downloadable!]
  18. Jingzhi Huang & Liuren Wu, 2004. "Specification Analysis of Option Pricing Models Based on Time- Changed Levy Processes," Finance 0401002, EconWPA. [Downloadable!]
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  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)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. David Backus & Mikhail Chernov & Ian Martin, 2009. "Disasters implied by equity index options," NBER Working Papers 15240, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  2. Prasad V. Bidarkota & Brice V. Dupoyet, 2004. "The Impact of Fat Tails on Equilibrium Rates of Return and Term Premia," Working Papers 0411, Florida International University, Department of Economics. [Downloadable!]
    Other versions:
  3. Zhiguang Wang & Prasad V. Bidarkota, 2008. "A Long-Run Risks Model of Asset Pricing with Fat Tails," Working Papers 0810, Florida International University, Department of Economics. [Downloadable!]
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