Pricing Illiquid Options with $N+1$ Liquid Proxies Using Mixed Dynamic-Static Hedging
AbstractWe 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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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1209.3503.
Date of creation: Sep 2012
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-09-30 (All new papers)
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- 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.
- Andrew Ang & Dimitris Papanikolaou & Mark Westerfield, 2013. "Portfolio Choice with Illiquid Assets," NBER Working Papers 19436, National Bureau of Economic Research, Inc.
- Andrey Itkin & Peter Carr, 2010.
"Using pseudo-parabolic and fractional equations for option pricing in jump diffusion models,"
- Andrey Itkin & Peter Carr, 2012. "Using Pseudo-Parabolic and Fractional Equations for Option Pricing in Jump Diffusion Models," Computational Economics, Society for Computational Economics, vol. 40(1), pages 63-104, June.
- 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.
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