Dynamic Hedging in Incomplete Markets: A Simple Solution

51 Pages Posted: 26 May 2011

See all articles by Suleyman Basak

Suleyman Basak

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

Georgy Chabakauri

London School of Economics and Political Science

Multiple version iconThere are 2 versions of this paper

Date Written: May 2011


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

JEL Classification: C61, D81, G11

Suggested Citation

Basak, Suleyman and Chabakauri, Georgy, Dynamic Hedging in Incomplete Markets: A Simple Solution (May 2011). CEPR Discussion Paper No. DP8402. Available at SSRN: https://ssrn.com/abstract=1853131

Suleyman Basak (Contact Author)

London Business School ( email )

Sussex Place
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London, London NW1 4SA
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HOME PAGE: http://www.suleymanbasak.com

Centre for Economic Policy Research (CEPR)

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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