PRICING ILLIQUID OPTIONS WITH N + 1 LIQUID PROXIES USING MIXED DYNAMIC-STATIC HEDGING

Igor Halperin () and Andrey Itkin ()
Additional contact information
Igor Halperin: JPMorgan Chase, 270 Park Avenue, New York, NY 10172, USA;

International Journal of Theoretical and Applied Finance (IJTAF), 2013, vol. 16, issue 07, 1-17

Abstract: We study the problem of the 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 Pi, each written on a liquid asset Yi, 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 an 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), and 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 model, the same approach can be used for other asset classes (equities, commodities, foreign exchange, and so on), for example, for pricing and hedging options with illiquid strikes or illiquid exotic options.

Keywords: Incomplete market; indifference pricing; illiquid option; dynamic/static hedge; HJB equation; operator splitting method (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0219024913500337
Access to full text is restricted to subscribers

Related works:
Working Paper: Pricing Illiquid Options with $N+1$ Liquid Proxies Using Mixed Dynamic-Static Hedging (2012)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijtafx:v:16:y:2013:i:07:n:s0219024913500337

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0219024913500337

Access Statistics for this article

International Journal of Theoretical and Applied Finance (IJTAF) is currently edited by L P Hughston

More articles in International Journal of Theoretical and Applied Finance (IJTAF) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().