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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Financial Markets Group in its series FMG Discussion Papers with number dp680.
Date of creation: May 2011
Date of revision:
Contact details of provider:
Web page: http://www.lse.ac.uk/fmg/
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.
- Georgy chabakauri & Suleyman Basak, 2009. "Dynamic Hedging in Incomplete Markets: A Simple Solution," 2009 Meeting Papers 594, Society for Economic Dynamics.
- Basak, Suleyman & Chabakauri, Georgy, 2011. "Dynamic Hedging in Incomplete Markets: A Simple Solution," CEPR Discussion Papers 8402, C.E.P.R. Discussion Papers.
- 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)
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.:
- 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.
- 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.
- Bossaerts, P. & Hillion, P., 1995.
"Local Parametric Analysis of Hedging in Discrete Time,"
1995-23, Tilburg University, Center for Economic Research.
- Bossaerts, Peter & Hillion, Pierre, 1997. "Local parametric analysis of hedging in discrete time," Journal of Econometrics, Elsevier, vol. 81(1), pages 243-272, November.
- Costa, O. L. V. & Paiva, A. C., 2002. "Robust portfolio selection using linear-matrix inequalities," Journal of Economic Dynamics and Control, Elsevier, vol. 26(6), pages 889-909, June.
- Anderson, Ronald W & Danthine, Jean-Pierre, 1980. " Hedging and Joint Production: Theory and Illustrations," Journal of Finance, American Finance Association, vol. 35(2), pages 487-98, May.
- 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.
- Jérôme B. Detemple & René Garcia & Marcel Rindisbacher, 2000.
"A Monte-Carlo Method for Optimal Portfolios,"
CIRANO Working Papers
- 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.
- Suleyman Basak & Georgy Chabakauri, 2010.
"Dynamic Mean-Variance Asset Allocation,"
Review of Financial Studies,
Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
- Lioui, Abraham, 2013. "Time consistent vs. time inconsistent dynamic asset allocation: Some utility cost calculations for mean variance preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 37(5), pages 1066-1096.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (The FMG Administration).
If references are entirely missing, you can add them using this form.