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A Consistent Pricing Model for Index Options and Volatility Derivatives

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  • Cont, Rama

    (Center for Financial Engineering)

  • Kokholm, Thomas

    (Department of Business Studies, Aarhus School of Business)

Abstract

We propose and study a flexible modeling framework for the joint dynamics of an index and a set of forward variance swap rates written on this index, allowing options on forward variance swaps and options on the underlying index to be priced consistently. Our model reproduces various empirically observed properties of variance swap dynamics and allows for jumps in volatility and returns. An affine specification using L´evy processes as building blocks leads to analytically tractable pricing formulas for options on variance swaps as well as efficient numerical methods for pricing of European options on the underlying asset. The model has the convenient feature of decoupling the vanilla skews from spot/volatility correlations and allowing for different conditional correlations in large and small spot/volatility moves. We show that our model can simultaneously fit prices of European options on S&P 500 across strikes and maturities as well as options on the VIX volatility index. The calibration of the model is done in two steps, first by matching VIX option prices and then by matching prices of options on the underlying

Suggested Citation

  • Cont, Rama & Kokholm, Thomas, 2009. "A Consistent Pricing Model for Index Options and Volatility Derivatives," Finance Research Group Working Papers F-2009-05, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    • Handle: RePEc:hhb:aarbfi:2009-05
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    References listed on IDEAS

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    1. Rama Cont, 2008. "Frontiers in Quantitative Finance: credit risk and volatility modeling," Post-Print hal-00437588, HAL.
    2. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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    Cited by:

    1. Gianna Figa-Talamanca & Maria Letizia Guerra, 2012. "Market Application of the Fuzzy-Stochastic Approach in the Heston Option Pricing Model," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 62(2), pages 162-179, May.

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