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

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  • I. Halperin
  • A. Itkin

Abstract

We study the problem of 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 $P_i$, each written on a liquid asset $Y_i, i=1,N$. 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 a 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), which 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'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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File URL: http://arxiv.org/pdf/1209.3503
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Paper provided by arXiv.org in its series Papers with number 1209.3503.

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Date of creation: Sep 2012
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Handle: RePEc:arx:papers:1209.3503

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Web page: http://arxiv.org/

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  1. Andrey Itkin & Peter Carr, 2010. "Using pseudo-parabolic and fractional equations for option pricing in jump diffusion models," Papers 1002.1995, arXiv.org.
  2. Vicky Henderson & Gechun Liang, 2011. "A Multidimensional Exponential Utility Indifference Pricing Model with Applications to Counterparty Risk," Papers 1111.3856, arXiv.org, revised May 2014.
  3. Anders B. Trolle & Eduardo S. Schwartz, 2009. "Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4423-4461, November.
  4. Andrew Ang & Dimitris Papanikolaou & Mark Westerfield, 2013. "Portfolio Choice with Illiquid Assets," NBER Working Papers 19436, National Bureau of Economic Research, Inc.
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