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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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    Cited by:

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    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.
    3. 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.
    4. Rui Menezes & Sonia Bentes, 2016. "Hysteresis and Duration Dependence of Financial Crises in the US: Evidence from 1871-2016," Papers 1610.00259, arXiv.org.
    5. 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.
    6. 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.
    7. 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).
    8. 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.
    9. 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.
    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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