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Pricing Illiquid Options With N + 1 Liquid Proxies Using Mixed Dynamic-Static Hedging

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  • IGOR HALPERIN

    (JPMorgan Chase, 270 Park Avenue, New York, NY 10172, USA;
    Polytechnic Institute of New York University, 6 Metro Tech Center, RH 517E, Brooklyn NY 11201, USA)

  • ANDREY ITKIN

    (Numerix LLC, 150 East 42nd Street, 15th Floor, New York, NY 10017, USA;
    Polytechnic Institute of New York University, 6 Metro Tech Center, RH 517E, Brooklyn NY 11201, USA)

Abstract

We study the problem of the optimal pricing and hedging of a European option written on an illiquid asset Z using a set of proxies: a liquid asset S, and N liquid European options Pi, each written on a liquid asset Yi, i = 1, N. We assume that the S-hedge is dynamic while the multi-name Y-hedge is static. Using the indifference pricing approach with an exponential utility, we derive an HJB equation for the value function, and build an efficient numerical algorithm. The latter is based on several changes of variables, a splitting scheme, and a set of fast Gauss Transforms (FGT), and turns out to be more efficient in terms of complexity and lower local space error than a finite-difference method. While in this paper we apply our framework to an incomplete market version of the credit-equity Merton model, the same approach can be used for other asset classes (equities, commodities, foreign exchange, and so on), for example, for pricing and hedging options with illiquid strikes or illiquid exotic options.

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  • Igor Halperin & Andrey Itkin, 2013. "Pricing Illiquid Options With N + 1 Liquid Proxies Using Mixed Dynamic-Static Hedging," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(07), pages 1-17.
    • Handle: RePEc:wsi:ijtafx:v:16:y:2013:i:07:n:s0219024913500337
    DOI: 10.1142/S0219024913500337
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    1. Anders B. Trolle & Eduardo S. Schwartz, 2009. "Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives," The Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4423-4461, November.
    2. Igor Halperin & Andrey Itkin, 2013. "Pricing Illiquid Options With N + 1 Liquid Proxies Using Mixed Dynamic-Static Hedging," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(07), pages 1-17.
    3. Igor Halperin & Andrey Itkin, 2014. "Pricing options on illiquid assets with liquid proxies using utility indifference and dynamic-static hedging," Quantitative Finance, Taylor & Francis Journals, vol. 14(3), pages 427-442, March.
    4. Andrew Ang & Dimitris Papanikolaou & Mark M. Westerfield, 2014. "Portfolio Choice with Illiquid Assets," Management Science, INFORMS, vol. 60(11), pages 2737-2761, November.
    5. Vicky Henderson & Gechun Liang, 2011. "A Multidimensional Exponential Utility Indifference Pricing Model with Applications to Counterparty Risk," Papers 1111.3856, arXiv.org, revised Sep 2015.
    6. Andrey Itkin & Peter Carr, 2012. "Using Pseudo-Parabolic and Fractional Equations for Option Pricing in Jump Diffusion Models," Computational Economics, Springer;Society for Computational Economics, vol. 40(1), pages 63-104, June.
    7. S. Narayan, 2009. "India," Chapters, in: Peter Draper & Philip Alves & Razeen Sally (ed.), The Political Economy of Trade Reform in Emerging Markets, chapter 7, Edward Elgar Publishing.
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    1. Igor Halperin & Andrey Itkin, 2013. "Pricing Illiquid Options With N + 1 Liquid Proxies Using Mixed Dynamic-Static Hedging," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(07), pages 1-17.

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