Pricing Illiquid Options with $N+1$ Liquid Proxies Using Mixed Dynamic-Static Hedging
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.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Vicky Henderson & Gechun Liang, 2011. "A Multidimensional Exponential Utility Indifference Pricing Model with Applications to Counterparty Risk," Papers 1111.3856, arXiv.org, revised Sep 2015.
- Andrey Itkin & Peter Carr, 2012.
"Using Pseudo-Parabolic and Fractional Equations for Option Pricing in Jump Diffusion Models,"
Springer;Society for Computational Economics, vol. 40(1), pages 63-104, June.
- Andrey Itkin & Peter Carr, 2010. "Using pseudo-parabolic and fractional equations for option pricing in jump diffusion models," Papers 1002.1995, arXiv.org.
- Igor Halperin & Andrey Itkin, 2014. "Pricing options on illiquid assets with liquid proxies using utility indifference and dynamic-static hedging," Quantitative Finance, Taylor & Francis Journals, vol. 14(3), pages 427-442, March.
- Igor Halperin & Andrey Itkin, 2012. "Pricing options on illiquid assets with liquid proxies using utility indifference and dynamic-static hedging," Papers 1205.3507, arXiv.org.
- S. Narayan, 2009. "India," Chapters, in: The Political Economy of Trade Reform in Emerging Markets, chapter 7 Edward Elgar Publishing.
- Andrew Ang & Dimitris Papanikolaou & Mark M. Westerfield, 2014. "Portfolio Choice with Illiquid Assets," Management Science, INFORMS, vol. 60(11), pages 2737-2761, November.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1209.3503. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If references are entirely missing, you can add them using this form.