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Pricing VIX options with stochastic volatility and random jumps

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  • Guang-Hua Lian
  • Song-Ping Zhu

Abstract

This study presents an analytical exact solution for the price of VIX options under stochastic volatility model with simultaneous jumps in the asset price and volatility processes. We shall demonstrate that our new pricing formula can be used to efficiently compute the numerical values of a VIX option. While we also show that the numerical results obtained from our formula consistently match those obtained from Monte Carlo simulation perfectly as a verification of the correctness of our formula, numerical evidence is offered to illustrate that the correctness of the formula proposed in Lin and Chang (J Futur Markets 29(6), 523–543, 2009 ) is in serious doubt. Moreover, some important and distinct properties of VIX options (e.g., put-call parity, hedging ratios) are also examined and discussed. Copyright Springer-Verlag 2013

Suggested Citation

  • Guang-Hua Lian & Song-Ping Zhu, 2013. "Pricing VIX options with stochastic volatility and random jumps," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 36(1), pages 71-88, May.
    • Handle: RePEc:spr:decfin:v:36:y:2013:i:1:p:71-88
    DOI: 10.1007/s10203-011-0124-0
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    References listed on IDEAS

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    1. 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.
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    3. Jin E. Zhang & Yuqin Huang, 2010. "The CBOE S&P 500 three‐month variance futures," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 30(1), pages 48-70, January.
    4. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    5. 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.
    6. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
    7. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
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    9. Peter Carr & Roger Lee, 2009. "Volatility Derivatives," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 319-339, November.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    VIX options; Heston model; Explicit and exact solution; Stochastic volatility; C2; C13;
    All these keywords.

    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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