Pricing options on illiquid assets with liquid proxies using utility indifference and dynamic-static hedging |
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Authors: | Igor Halperin Andrey Itkin |
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Affiliation: | 1. Model Risk &2. Development , JPMorgan Chase , 277 Park Avenue, New York , NY , 10172 , USA igor.halperin@jpmorgan.com;4. Department of Finance and Risk Engineering , NYU Polytechnic Institute , 6 Metro Tech Center, RH 517E, Brooklyn , NY , 11201 , USA |
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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. |
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Keywords: | Incomplete markets Asset pricing Derivative pricing models Quantitative finance techniques Hedging with utility based preferences Computational finance Pricing with utility based preferences |
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