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.
|Date of creation:||May 2011|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: 44 - 20 - 7183 8801
Fax: 44 - 20 - 7183 8820
|Order Information:|| Email: |
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.:
- Bossaerts, Peter & Hillion, Pierre, 1997. "Local parametric analysis of hedging in discrete time," Journal of Econometrics, Elsevier, vol. 81(1), pages 243-272, November.
- Jér�me 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.
- 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.
- 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.
- Bekaert, Geert & Harvey, Campbell R, 1995.
" Time-Varying World Market Integration,"
Journal of Finance,
American Finance Association, vol. 50(2), pages 403-44, June.
- 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.
- 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.
- 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.
- 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, June.
When requesting a correction, please mention this item's handle: RePEc:cpr:ceprdp:8402. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()The email address of this maintainer does not seem to be valid anymore. Please ask to update the entry or send us the correct address
If references are entirely missing, you can add them using this form.