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Static Hedging of Multivariate Derivatives by Simulation

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  • Paolo Pellizzari

    (University of Venice)

Abstract

We 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.

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File URL: http://128.118.178.162/eps/fin/papers/0311/0311013.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Finance with number 0311013.

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Length: 23 pages
Date of creation: 28 Nov 2003
Date of revision: 04 Dec 2003
Handle: RePEc:wpa:wuwpfi:0311013

Note: Type of Document - pdf; prepared on Latex on Mac; to print on Laser; pages: 23; figures: included
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Web page: http://128.118.178.162

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Keywords: Monte Carlo methods; option pricing; static and dynamic hedging;

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  1. 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.
  2. 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.
  3. 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.
  4. Hayne E. Leland., 1984. "Option Pricing and Replication with Transactions Costs," Research Program in Finance Working Papers 144, University of California at Berkeley.
  5. Hans FÃllmer & Peter Leukert, 2000. "Efficient hedging: Cost versus shortfall risk," Finance and Stochastics, Springer, vol. 4(2), pages 117-146.
  6. Boyle, Phelim P. & Emanuel, David, 1980. "Discretely adjusted option hedges," Journal of Financial Economics, Elsevier, vol. 8(3), pages 259-282, September.
  7. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
  8. 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.
  9. 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.
  10. Riccardo Rebonato & Ian Cooper, 1998. "Coupling backward induction with Monte Carlo simulations: a fast Fourier transform (FFT) approach," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(2), pages 131-141.
  11. 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.
  12. 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.
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Cited by:
  1. Xia Su, 2006. "Hedging Basket Options by Using a Subset of Underlying Assets," Bonn Econ Discussion Papers bgse14_2006, University of Bonn, Germany.
  2. 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.

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