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

Igor Halperin and Andrey Itkin ()

Quantitative Finance, 2014, vol. 14, issue 3, 427-442

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.

Date: 2014
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Working Paper: Pricing options on illiquid assets with liquid proxies using utility indifference and dynamic-static hedging (2012)
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DOI: 10.1080/14697688.2013.816766

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