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The Generalized Extreme Value (GEV) Distribution, Implied Tail Index and Option Pricing

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  • Sheri Markose

    ()

  • Amadeo Alentorn

    ()

Abstract

Crisis events such as the 1987 stock market crash, the Asian Crisis and the bursting of the Dot-Com bubble have radically changed the view that extreme events in financial markets have negligible probability. This paper argues that the use of the Generalized Extreme Value (GEV) distribution to model the Risk Neutral Density (RND) function provides a flexible framework that captures the negative skewness and excess kurtosis of returns, and also delivers the market implied tail index of asset returns. We obtain an original analytical closed form solution for the Harrison and Pliska (1981) no arbitrage equilibrium price for the European option in the case of GEV asset returns. The GEV based option prices successfully remove the well known pricing bias of the Black-Scholes model. We explain how the implied tail index is efficacious at identifying the fat tailed behaviour of losses and hence the left skewness of the price RND functions, particularly around crisis events.

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Bibliographic Info

Paper provided by University of Essex, Department of Economics in its series Economics Discussion Papers with number 594.

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Date of creation: 25 Apr 2005
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Handle: RePEc:esx:essedp:594

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  1. Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm54, Yale School of Management.
  2. Rubinstein, Mark, 1985. " Nonparametric Tests of Alternative Option Pricing Models Using All Reported Trades and Quotes on the 30 Most Active CBOE Option Classes from August 23, 1976 through August 31, 1978," Journal of Finance, American Finance Association, vol. 40(2), pages 455-80, June.
  3. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. " Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-32, December.
  4. Panigirtzoglou, Nikolaos & Skiadopoulos, George, 2004. "A new approach to modeling the dynamics of implied distributions: Theory and evidence from the S&P 500 options," Journal of Banking & Finance, Elsevier, vol. 28(7), pages 1499-1520, July.
  5. Karim Abadir & Michael Rockinger, . "Density-Embedding Functions," Discussion Papers 97/16, Department of Economics, University of York.
  6. Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm65, Yale School of Management.
  7. de Jong, C.M. & Huisman, R., 2000. "From Skews to a Skewed-t," ERIM Report Series Research in Management ERS-2000-12-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus Uni.
  8. Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, vol. 10(3), pages 347-369, November.
  9. William R. Melick & Charles P. Thomas, 1996. "Using options prices to infer PDF'S for asset prices: an application to oil prices during the Gulf crisis," International Finance Discussion Papers 541, Board of Governors of the Federal Reserve System (U.S.).
  10. Buchen, Peter W. & Kelly, Michael, 1996. "The Maximum Entropy Distribution of an Asset Inferred from Option Prices," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(01), pages 143-159, March.
  11. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-49, December.
  12. Yacine Ait-Sahalia & Andrew W. Lo, 2000. "Nonparametric Risk Management and Implied Risk Aversion," NBER Working Papers 6130, National Bureau of Economic Research, Inc.
  13. Jackwerth, Jens Carsten, 1999. "Option Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review," MPRA Paper 11634, University Library of Munich, Germany.
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Cited by:
  1. Sheri M. Markose, 2012. "Systemic Risk from Global Financial Derivatives," IMF Working Papers 12/282, International Monetary Fund.
  2. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.

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