Dynamic hedging in incomplete markets: a simple solution

Basak, Suleyman and Chabakauri, Georgy (2011) Dynamic hedging in incomplete markets: a simple solution. Financial Markets Group Discussion Papers (680). Financial Markets Group, The London School of Economics and Political Science, London, UK.

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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.

Item Type:	Monograph (Discussion Paper)
Official URL:	https://www.fmg.ac.uk/
Additional Information:	© 2011 The Authors
Divisions:	Finance
Subjects:	H Social Sciences > HC Economic History and Conditions H Social Sciences > HG Finance
JEL classification:	G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice; Investment Decisions D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty C - Mathematical and Quantitative Methods > C6 - Mathematical Methods and Programming > C61 - Optimization Techniques; Programming Models; Dynamic Analysis
Date Deposited:	04 Jul 2023 08:27
Last Modified:	16 Sep 2023 00:02
URI:	http://eprints.lse.ac.uk/id/eprint/119068

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