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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 Hamilton--Jacobi--Bellman equation for the value function. We solve this equation analytically (in quadrature) using an asymptotic expansion around the limit of perfect correlation between assets Y and Z. While in this paper we apply our framework to an incomplete market version of Merton's credit-equity 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.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:quantf:v:14:y:2014:i:3:p:427-442
    DOI: 10.1080/14697688.2013.816766
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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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    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.
    2. Jarno Talponen, 2018. "Matching distributions: Recovery of implied physical densities from option prices," Papers 1803.03996, arXiv.org.
    3. Chuang, Ming-Che & Tsai, Jeffrey Tzuhao, 2024. "Determining bid-ask prices for options with stochastic illiquidity and applications to index options," Pacific-Basin Finance Journal, Elsevier, vol. 84(C).

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