Dynamic Hedging in Incomplete Markets: A Simple Solution
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.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- GEORGE W. EVANS & BRUCE McGOUGH, 2007.
"Optimal Constrained Interest-Rate Rules,"
Journal of Money, Credit and Banking,
Blackwell Publishing, vol. 39(6), pages 1335-1356, 09.
- Bruce McGough & George Evans, 2004. "Optimal Constrained Interest Rate Rules," Computing in Economics and Finance 2004 134, Society for Computational Economics.
- George W. Evans & Bruce McGough, 2005. "Optimal Constrained Interest-rate Rules," University of Oregon Economics Department Working Papers 2005-9, University of Oregon Economics Department, revised 31 May 2006.
- Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
- Jérôme B. Detemple & René Garcia & Marcel Rindisbacher, 2003. "A Monte Carlo Method for Optimal Portfolios," Journal of Finance, American Finance Association, vol. 58(1), pages 401-446, 02.
- Jérôme B. Detemple & René Garcia & Marcel Rindisbacher, 2000. "A Monte-Carlo Method for Optimal Portfolios," CIRANO Working Papers 2000s-05, CIRANO.
- Bekaert, Geert & Harvey, Campbell R, 1995. " Time-Varying World Market Integration," Journal of Finance, American Finance Association, vol. 50(2), pages 403-444, June.
- Geert Bekaert & Campbell R. Harvey, 1994. "Time-Varying World Market Integration," NBER Working Papers 4843, National Bureau of Economic Research, Inc.
- Andrea Buraschi & Paolo Porchia & Fabio Trojani, 2010. "Correlation Risk and Optimal Portfolio Choice," Journal of Finance, American Finance Association, vol. 65(1), pages 393-420, 02.
- Bossaerts, Peter & Hillion, Pierre, 1997. "Local parametric analysis of hedging in discrete time," Journal of Econometrics, Elsevier, vol. 81(1), pages 243-272, November.
- Joost Driessen & Pascal J. Maenhout & Grigory Vilkov, 2009. "The Price of Correlation Risk: Evidence from Equity Options," Journal of Finance, American Finance Association, vol. 64(3), pages 1377-1406, 06.
- Jaksa Cvitanic & Fernando Zapatero, 2004. "Introduction to the Economics and Mathematics of Financial Markets," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262532654. Full references (including those not matched with items on IDEAS)