Static Hedging of Multivariate Derivatives by Simulation
AbstractWe propose an approximate static hedging procedure for multivariate derivatives. The hedging portfolio is composed of statically held simple univariate options, optimally weighted minimizing the variance of the difference between the target claim and the approximate replicating portfolio. The method uses simulated paths to estimate the weights of the hedging portfolio and is related to Monte Carlo control variates techniques. We report numerical results showing the performance of this static hedging procedure on bivariate options on the maximum of two assets and on 2- and 7-dimensional portfolio options. It is shown that, in the presence of transaction costs, Value at Risk and Expected Shortfall of the dynamically hedged positions can be higher than the ones obtained by a static hedge.
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 EconWPA in its series Finance with number 0311013.
Length: 23 pages
Date of creation: 28 Nov 2003
Date of revision: 04 Dec 2003
Note: Type of Document - pdf; prepared on Latex on Mac; to print on Laser; pages: 23; figures: included
Contact details of provider:
Web page: http://188.8.131.52
Monte Carlo methods; option pricing; static and dynamic hedging;
Other versions of this item:
- Pellizzari, P., 2005. "Static hedging of multivariate derivatives by simulation," European Journal of Operational Research, Elsevier, vol. 166(2), pages 507-519, October.
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
This paper has been announced in the following NEP Reports:
- NEP-ALL-2003-11-30 (All new papers)
- NEP-CFN-2003-11-30 (Corporate Finance)
- NEP-CMP-2003-11-30 (Computational Economics)
- NEP-FIN-2003-11-30 (Finance)
- NEP-RMG-2003-11-30 (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.:
- Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
- Boyle, Phelim P. & Emanuel, David, 1980. "Discretely adjusted option hedges," Journal of Financial Economics, Elsevier, vol. 8(3), pages 259-282, September.
- Y. M. Kabanov & M. Safarian, 1995.
"On Leland's Strategy of Option Pricing with Transaction Costs,"
SFB 373 Discussion Papers
1995,65, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Yuri M. Kabanov & (*), Mher M. Safarian, 1997. "On Leland's strategy of option pricing with transactions costs," Finance and Stochastics, Springer, vol. 1(3), pages 239-250.
- Boyle, Phelim P., 1988. "A Lattice Framework for Option Pricing with Two State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(01), pages 1-12, March.
- Hyungsok Ahn Adviti & Glen Swindle, 1997. "Misspecified asset price models and robust hedging strategies," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(1), pages 21-36.
- Peter Carr & Katrina Ellis & Vishal Gupta, 1998. "Static Hedging of Exotic Options," Journal of Finance, American Finance Association, vol. 53(3), pages 1165-1190, 06.
- T. Clifton Green & Stephen Figlewski, 1999. "Market Risk and Model Risk for a Financial Institution Writing Options," Journal of Finance, American Finance Association, vol. 54(4), pages 1465-1499, 08.
- S. S. Lavenberg & P. D. Welch, 1981. "A Perspective on the Use of Control Variables to Increase the Efficiency of Monte Carlo Simulations," Management Science, INFORMS, vol. 27(3), pages 322-335, March.
- Leland, Hayne E, 1985.
" Option Pricing and Replication with Transactions Costs,"
Journal of Finance,
American Finance Association, vol. 40(5), pages 1283-1301, December.
- Hayne E. Leland., 1984. "Option Pricing and Replication with Transactions Costs," Research Program in Finance Working Papers 144, University of California at Berkeley.
- Hans FÃllmer & Peter Leukert, 2000. "Efficient hedging: Cost versus shortfall risk," Finance and Stochastics, Springer, vol. 4(2), pages 117-146.
- Stulz, ReneM., 1982. "Options on the minimum or the maximum of two risky assets : Analysis and applications," Journal of Financial Economics, Elsevier, vol. 10(2), pages 161-185, July.
- Xia Su, 2006. "Hedging Basket Options by Using a Subset of Underlying Assets," Bonn Econ Discussion Papers bgse14_2006, University of Bonn, Germany.
- Johannes Siven & Rolf Poulsen, 2009. "Auto-static for the people: risk-minimizing hedges of barrier options," Review of Derivatives Research, Springer, vol. 12(3), pages 193-211, October.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA).
If references are entirely missing, you can add them using this form.