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

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  • Markose, Sheri M
  • Alentorn, Amadeo

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.

Suggested Citation

  • Markose, Sheri M & Alentorn, Amadeo, 2005. "The Generalized Extreme Value (GEV) Distribution, Implied Tail Index and Option Pricing," Economics Discussion Papers 3726, University of Essex, Department of Economics.
    • Handle: RePEc:esx:essedp:3726
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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Lux, Thomas & Sornette, Didier, 2002. "On Rational Bubbles and Fat Tails," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 34(3), pages 589-610, August.
    3. 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 University Rotterdam.
    4. C. J. Corrado & Tie Su, 1997. "Implied volatility skews and stock return skewness and kurtosis implied by stock option prices," The European Journal of Finance, Taylor & Francis Journals, vol. 3(1), pages 73-85, March.
    5. Bali, Turan G., 2003. "The generalized extreme value distribution," Economics Letters, Elsevier, vol. 79(3), pages 423-427, June.
    6. Robert Savickas, 2002. "A Simple Option‐Pricing Formula," The Financial Review, Eastern Finance Association, vol. 37(2), pages 207-226, May.
    7. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. 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(1), pages 143-159, March.
    9. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    10. Charles J. Corrado, 2001. "Option pricing based on the generalized lambda distribution," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 21(3), pages 213-236, March.
    11. Jackwerth, Jens Carsten, 1999. "Option Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review," MPRA Paper 11634, University Library of Munich, Germany.
    12. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    13. 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 455-480, June.
    14. Ritchey, Robert J, 1990. "Call Option Valuation for Discrete Normal Mixtures," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 13(4), pages 285-296, Winter.
    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 637-654, May-June.
    16. Robert JARROW & Andrew RUDD, 2008. "Approximate Option Valuation For Arbitrary Stochastic Processes," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 1, pages 9-31, World Scientific Publishing Co. Pte. Ltd..
    17. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    18. 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.
    19. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. "Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-1632, December.
    20. Carmela Quintos & Zhenhong Fan & Peter C. B. Phillips, 2001. "Structural Change Tests in Tail Behaviour and the Asian Crisis," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(3), pages 633-663.
    21. repec:bla:jfinan:v:59:y:2004:i:1:p:407-446 is not listed on IDEAS
    22. Robert J. Ritchey, 1990. "Call Option Valuation For Discrete Normal Mixtures," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 13(4), pages 285-296, December.
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    Cited by:

    1. 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.
    2. Rui Menezes & Sonia Bentes, 2016. "Hysteresis and Duration Dependence of Financial Crises in the US: Evidence from 1871-2016," Papers 1610.00259, arXiv.org.
    3. Marcos Massaki Abe & Eui Jung Chang & Benjamin Miranda Tabak, 2007. "Forecasting Exchange Rate Density Using Parametric Models: the Case of Brazil," Brazilian Review of Finance, Brazilian Society of Finance, vol. 5(1), pages 29-39.
    4. Ms. Sheri M. Markose, 2012. "Systemic Risk from Global Financial Derivatives: A Network Analysis of Contagion and Its Mitigation with Super-Spreader Tax," IMF Working Papers 2012/282, International Monetary Fund.
    5. repec:grz:wpaper:2012-05 is not listed on IDEAS
    6. Joocheol Kim & HyunOh Kim, 2014. "Option Pricing with Generalized Logistic Distributions(published in:Global Economic Review, (2014) Vol.43, NO.3)," Working papers 2014rwp-66, Yonsei University, Yonsei Economics Research Institute.
    7. Joocheol Kim & Jeonggyu Heo, 2014. "Option Pricing with Heavy Tailed Distribution : Application to Barrier Options," Working papers 2014rwp-73, Yonsei University, Yonsei Economics Research Institute.
    8. Bari, Chintaman Santosh & Chandra, Satish & Dhamaniya, Ashish, 2022. "Service headway distribution analysis of FASTag lanes under mixed traffic conditions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    9. Alentorn, Amadeo & Markose, Sheri M, 2006. "Removing Maturity Effects of Implied Risk Neutral Densities and Related Statistics," Economics Discussion Papers 3722, University of Essex, Department of Economics.
    10. Frank Fabozzi & Radu Tunaru & George Albota, 2009. "Estimating risk-neutral density with parametric models in interest rate markets," Quantitative Finance, Taylor & Francis Journals, vol. 9(1), pages 55-70.

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