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Pricing Joint Claims On An Asset And Its Realized Variance In Stochastic Volatility Models

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  • LORENZO TORRICELLI

    (Department of Mathematics, University College London, Gower Street WC1E 6BT, London, UK)

Abstract

In the setting of a stochastic volatility model, 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 provides a pricing tool for European-style claims paying off at maturity a joint function of the underlying and its realized volatility or variance. We study the solution under various specific 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 valued by means of the general pricing equation. Numerical results are given and compared to those from plain vanilla derivatives.

Suggested Citation

  • Lorenzo Torricelli, 2013. "Pricing Joint Claims On An Asset And Its Realized Variance In Stochastic Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 1-18.
    • Handle: RePEc:wsi:ijtafx:v:16:y:2013:i:01:n:s0219024913500052
    DOI: 10.1142/S0219024913500052
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    References listed on IDEAS

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    1. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
    2. Alexander Lipton, 2001. "Mathematical Methods for Foreign Exchange:A Financial Engineer's Approach," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 4694, February.
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    Cited by:

    1. Elisa Alos & Rupak Chatterjee & Sebastian Tudor & Tai-Ho Wang, 2018. "Target volatility option pricing in lognormal fractional SABR model," Papers 1801.08215, arXiv.org.
    2. Wang, Xingchun, 2021. "Pricing volatility-equity options under the modified constant elasticity of variance model," Finance Research Letters, Elsevier, vol. 38(C).
    3. Hongkai Cao & Alexandru Badescu & Zhenyu Cui & Sarath Kumar Jayaraman, 2020. "Valuation of VIX and target volatility options with affine GARCH models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(12), pages 1880-1917, December.
    4. Lorenzo Torricelli, 2016. "Valuation of asset and volatility derivatives using decoupled time-changed Lévy processes," Review of Derivatives Research, Springer, vol. 19(1), pages 1-39, April.

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