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Pricing options on illiquid assets with liquid proxies using utility indifference and dynamic-static hedging

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  • Igor Halperin
  • Andrey Itkin

Abstract

This work addresses the problem of optimal pricing and hedging of a European option on an illiquid asset Z using two proxies: a liquid asset S and a liquid European option on another liquid asset Y. We assume that the S-hedge is dynamic while the Y-hedge is static. Using the indifference pricing approach we derive a HJB equation for the value function, and solve it analytically (in quadratures) using an asymptotic expansion around the limit of the perfect correlation between assets Y and Z. While in this paper we apply our framework to an incomplete market version of the credit-equity Merton's model, the same approach can be used for other asset classes (equity, commodity, FX, etc.), e.g. for pricing and hedging options with illiquid strikes or illiquid exotic options.

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  • Igor Halperin & Andrey Itkin, 2012. "Pricing options on illiquid assets with liquid proxies using utility indifference and dynamic-static hedging," Papers 1205.3507, arXiv.org.
    • Handle: RePEc:arx:papers:1205.3507
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    References listed on IDEAS

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    1. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
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    Cited by:

    1. Jarno Talponen, 2018. "Matching distributions: Recovery of implied physical densities from option prices," Papers 1803.03996, arXiv.org.
    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.

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