Dynamic Hedging in Incomplete Markets: A Simple Solution
AbstractDespite 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.
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Bibliographic InfoPaper provided by Financial Markets Group in its series FMG Discussion Papers with number dp680.
Date of creation: May 2011
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Other versions of this item:
- Suleyman Basak & Georgy Chabakauri, 2012. "Dynamic Hedging in Incomplete Markets: A Simple Solution," Review of Financial Studies, Society for Financial Studies, vol. 25(6), pages 1845-1896.
- Basak, Suleyman & Chabakauri, Georgy, 2011. "Dynamic Hedging in Incomplete Markets: A Simple Solution," CEPR Discussion Papers 8402, C.E.P.R. Discussion Papers.
- Georgy chabakauri & Suleyman Basak, 2009. "Dynamic Hedging in Incomplete Markets: A Simple Solution," 2009 Meeting Papers 594, Society for Economic Dynamics.
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-04-10 (All new papers)
- NEP-FMK-2012-04-10 (Financial Markets)
- NEP-RMG-2012-04-10 (Risk Management)
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