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Pricing joint claims on an asset and its realized variance under stochastic volatility models

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  • Lorenzo Torricelli

Abstract

In a stochastic volatility framework, we find a general pricing equation for the class of payoffs depending on the terminal value of a market asset and its final quadratic variation. This allows a pricing tool for European-style claims paying off at maturity a joint function of the underlying and its realised volatility/variance. We study the solution under different stochastic volatility models, give a formula for the computation of the Delta and Gamma of these claims, and introduce some new interesting payoffs that can be priced through this equation. Numerical results are given and compared to those from plain vanilla derivatives.

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  • Lorenzo Torricelli, 2012. "Pricing joint claims on an asset and its realized variance under stochastic volatility models," Papers 1206.2112, arXiv.org.
    • Handle: RePEc:arx:papers:1206.2112
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    References listed on IDEAS

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    1. Bergman, Yaacov Z & Grundy, Bruce D & Wiener, Zvi, 1996. "General Properties of Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1573-1610, December.
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    3. Giuseppe Di Graziano & Lorenzo Torricelli, 2012. "Target Volatility Option Pricing," World Scientific Book Chapters, in: Matheus R Grasselli & Lane P Hughston (ed.), Finance at Fields, chapter 8, pages 207-223, World Scientific Publishing Co. Pte. Ltd..
    4. 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.
    5. Leif Andersen & Vladimir Piterbarg, 2007. "Moment explosions in stochastic volatility models," Finance and Stochastics, Springer, vol. 11(1), pages 29-50, January.
    6. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
    7. Robert Elliott & Tak Kuen Siu & Leunglung Chan, 2007. "Pricing Volatility Swaps Under Heston's Stochastic Volatility Model with Regime Switching," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(1), pages 41-62.
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    Cited by:

    1. Lorenzo Torricelli, 2012. "Valuation of asset and volatility derivatives using decoupled time-changed L\'evy processes," Papers 1210.5479, arXiv.org, revised Jan 2015.

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