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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- Andrey Itkin & Peter Carr, 2010.
"Using pseudo-parabolic and fractional equations for option pricing in jump diffusion models,"
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