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Target Volatility Option Pricing

Author

Listed:
  • GIUSEPPE DI GRAZIANO

    (Deutsche Bank AG, UK;
    Department of Mathematics, King's College London, Strand, London, WC2R 2LS, UK)

  • LORENZO TORRICELLI

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

Abstract

In this paper we present two methods for the pricing of Target Volatility Options (TVOs), a recent market innovation in the field of volatility derivative. TVOs allow investors to take a joint view on the future price of a given underlying (e.g. stocks, commodities, etc) and its realized volatility. For example, a target volatility call pays at maturity the terminal value of the asset minus the strike, floored at zero, scaled by the ratio of the target volatility (an arbitrary constant) and the realized volatility of the underlying over the life of the option. TVOs are popular with investors and hedgers because they are typically cheaper than their vanilla equivalent. We present two approaches for the pricing of TVOs: a power series expansion and a Laplace transform method. We also provide both model dependent and model independent solutions. The pricing methodologies have been tested numerically and results are provided.

Suggested Citation

  • Giuseppe Di Graziano & Lorenzo Torricelli, 2012. "Target Volatility Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-17.
    • Handle: RePEc:wsi:ijtafx:v:15:y:2012:i:01:n:s0219024911006474
    DOI: 10.1142/S0219024911006474
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    References listed on IDEAS

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    1. Arturo Estrella, 1995. "Taylor, Black and Scholes: series approximations and risk management pitfalls," Research Paper 9501, Federal Reserve Bank of New York.
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    Cited by:

    1. Wang, Xingchun, 2021. "Pricing volatility-equity options under the modified constant elasticity of variance model," Finance Research Letters, Elsevier, vol. 38(C).
    2. 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.
    3. 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.
    4. Elisa Alos & Rupak Chatterjee & Sebastian Tudor & Tai-Ho Wang, 2018. "Target volatility option pricing in lognormal fractional SABR model," Papers 1801.08215, arXiv.org.
    5. Roberto Daluiso & Emanuele Nastasi & Andrea Pallavicini & Stefano Polo, 2021. "Reinforcement learning for options on target volatility funds," Papers 2112.01841, arXiv.org.
    6. Ma, Jingtang & Li, Wenyuan & Han, Xu, 2015. "Stochastic lattice models for valuation of volatility options," Economic Modelling, Elsevier, vol. 47(C), pages 93-104.
    7. Wang, Xingchun, 2016. "Catastrophe equity put options with target variance," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 79-86.

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