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Static hedging of multivariate derivatives by simulation

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  • Pellizzari, P.

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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  • Pellizzari, P., 2005. "Static hedging of multivariate derivatives by simulation," European Journal of Operational Research, Elsevier, vol. 166(2), pages 507-519, October.
    • Handle: RePEc:eee:ejores:v:166:y:2005:i:2:p:507-519
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    Cited by:

    1. Hachmi Ben Ameur & Mouna Boujelbène & J. L. Prigent & Emna Triki, 2020. "Optimal Portfolio Positioning on Multiple Assets Under Ambiguity," Computational Economics, Springer;Society for Computational Economics, vol. 56(1), pages 21-57, June.
    2. Dirk Becherer & Ian Ward, 2010. "Optimal Weak Static Hedging of Equity and Credit Risk Using Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(1), pages 1-28.
    3. Vikranth Lokeshwar & Vikram Bhardawaj & Shashi Jain, 2019. "Neural network for pricing and universal static hedging of contingent claims," Papers 1911.11362, arXiv.org.
    4. 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.
    5. Lokeshwar, Vikranth & Bharadwaj, Vikram & Jain, Shashi, 2022. "Explainable neural network for pricing and universal static hedging of contingent claims," Applied Mathematics and Computation, Elsevier, vol. 417(C).

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    More about this item

    JEL classification:

    • 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

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