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Option Pricing with Normal Mixture Returns: Modelling Excess Kurtosis and Uncertanity in Volatility

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  • Carol Alexander

    (ICMA Centre, University of Reading)

  • Sujit Narayanan

    (ICMA Centre, University of Reading)

Abstract

his paper addresses the problem of uncertainty in volatility, and how this affects option prices. The volatility uncertainty adjustment to Black-Scholes option prices is quantified in this paper using a normal mixture model for the distribution of underlying returns, or equivalently, assuming a mixture of lognormal densities for the density of the asset price. The use of a lognormal mixture price process for pricing options is not new (Ritchey, 1990) but the local volatility that should be used in the lognormal mixture price process has only recently been established (Brigo and Mercurio, 2000a, 2001).Â

Suggested Citation

  • Carol Alexander & Sujit Narayanan, 2001. "Option Pricing with Normal Mixture Returns: Modelling Excess Kurtosis and Uncertanity in Volatility," ICMA Centre Discussion Papers in Finance icma-dp2001-10, Henley Business School, University of Reading, revised Dec 2001.
    • Handle: RePEc:rdg:icmadp:icma-dp2001-10
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    File URL: http://www.icmacentre.ac.uk/pdf/discussion/DP2001-10.pdf
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    References listed on IDEAS

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    Cited by:

    1. Kole, H.J.W.G. & Koedijk, C.G. & Verbeek, M.J.C.M., 2004. "The effects of systemic crises when investors can be crisis ignorant," ERIM Report Series Research in Management ERS-2004-027-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.
    2. En-Der Su & Feng-Jeng Lin, 2012. "Two-State Volatility Transition Pricing and Hedging of TXO Options," Computational Economics, Springer;Society for Computational Economics, vol. 39(3), pages 259-287, March.
    3. Halperin, Igor, 2022. "Non-equilibrium skewness, market crises, and option pricing: Non-linear Langevin model of markets with supersymmetry," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 594(C).
    4. Damiano Brigo, 2008. "The general mixture-diffusion SDE and its relationship with an uncertain-volatility option model with volatility-asset decorrelation," Papers 0812.4052, arXiv.org.
    5. Fleming, Jeff & Paye, Bradley S., 2011. "High-frequency returns, jumps and the mixture of normals hypothesis," Journal of Econometrics, Elsevier, vol. 160(1), pages 119-128, January.
    6. Igor Halperin, 2020. "Non-Equilibrium Skewness, Market Crises, and Option Pricing: Non-Linear Langevin Model of Markets with Supersymmetry," Papers 2011.01417, arXiv.org, revised Dec 2021.

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