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Dynamic Hedging in Incomplete Markets: A Simple Solution

49 Pages Posted: 7 Nov 2008 Last revised: 12 May 2011

Suleyman Basak

London Business School; Centre for Economic Policy Research (CEPR)

Georgy Chabakauri

London School of Economics and Political Science

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Date Written: May 9, 2011

Abstract

Despite much work on hedging in incomplete markets, the literature still lacks tractable dynamic hedges in plausible environments. In this article, we provide a simple solution to this problem in a general incomplete-market economy in which a hedger, guided by the traditional minimum-variance criterion, aims at reducing the risk of a non-tradable asset or a contingent claim. We derive fully analytical optimal hedges and demonstrate that they can easily be computed in various stochastic environments. Our dynamic hedges preserve the simple structure of complete-market perfect hedges and are in terms of generalized "Greeks," familiar in risk management applications, as well as retaining the intuitive features of their static counterparts. We obtain our time-consistent hedges by dynamic programming, while the extant literature characterizes either static or myopic hedges, or dynamic ones that minimize the variance criterion at an initial date and from which the hedger may deviate unless she can pre-commit to follow them. We apply our results to the discrete hedging problem of derivatives when trading occurs infrequently. We determine the corresponding optimal hedge and replicating portfolio value, and show that they have structure similar to their complete-market counterparts and reduce to generalized Black-Scholes expressions when specialized to the Black-Scholes setting. We also generalize our results to richer settings to study dynamic hedging with Poisson jumps, stochastic correlation and portfolio management with benchmarking.

Keywords: Hedging, incomplete markets, minimum-variance criterion, risk management, time-consistency, discrete hedging, derivatives, benchmarking, correlation risk, Poisson jumps

JEL Classification: G11, D81, C61

Suggested Citation

Basak, Suleyman and Chabakauri, Georgy, Dynamic Hedging in Incomplete Markets: A Simple Solution (May 9, 2011). EFA 2009 Bergen Meetings Paper; AFA 2012 Chicago Meetings Paper. Available at SSRN: https://ssrn.com/abstract=1297182 or http://dx.doi.org/10.2139/ssrn.1297182

Suleyman Basak (Contact Author)

London Business School ( email )

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London, London NW1 4SA
United Kingdom
44 (0)20 7000 8256 (Phone)
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HOME PAGE: http://www.suleymanbasak.com

Centre for Economic Policy Research (CEPR)

77 Bastwick Street
London, EC1V 3PZ
United Kingdom

Georgy Chabakauri

London School of Economics and Political Science ( email )

Houghton Street
London, WC2A 2AE
United Kingdom

HOME PAGE: http://personal.lse.ac.uk/CHABAKAU/

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