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Numerical Valuation of High Dimensional Multivariate European Securities

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  • Jèôme Barraquand

    (Salomon Brothers International Ltd., Victoria Plaza, 111 Buckingham Palace Road, London SW1W 0SB, United Kingdom)

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    Abstract

    We consider the problem of pricing a contingent claim whose payoff depends on several sources of uncertainty. Using classical assumptions from the Arbitrage Pricing Theory, the theoretical price can be computed as the discounted expected value of future cash flows under the modified risk-neutral information process. Although analytical solutions have been developed elsewhere for a few particular option pricing problems, computing the arbitrage prices of securities under several sources of uncertainty is still an open problem in many instances. In this paper, we present efficient numerical techniques based upon Monte Carlo simulation for pricing European contingent claims depending on an arbitrary number of risk sources. We introduce in particular the method of quadratic resampling (QR), a new powerful error reduction technique for Monte Carlo simulation. Quadratic resampling can be efficiently combined with classical variance reduction methods such as importance sampling. Our numerical experiments show that the method is practical for pricing claims depending on up to one hundred underlying assets.

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    File URL: http://dx.doi.org/10.1287/mnsc.41.12.1882
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 41 (1995)
    Issue (Month): 12 (December)
    Pages: 1882-1891

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    Handle: RePEc:inm:ormnsc:v:41:y:1995:i:12:p:1882-1891

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    Related research

    Keywords: option pricing; multidimensional contingent claims; Monte Carlo method; importance sampling; quadratic resampling;

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    Cited by:
    1. Ng, Andrew C.Y. & Li, Johnny Siu-Hang & Chan, Wai-Sum, 2013. "Pricing options on stocks denominated in different currencies: Theory and illustrations," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 339-354.
    2. Robert H. Keeley & Sanjeev Punjabi & Lassaad Turki, 1996. "Valuation of Early-Stage Ventures: Option Valuation Models vs. Traditional Approaches," Journal of Entrepreneurial Finance, Pepperdine University, Graziadio School of Business and Management, vol. 5(2), pages 115-38 , Summer.
    3. Tommaso Paletta & Arturo Leccadito & Radu Tunaru, 2013. "Pricing and Hedging Basket Options with Exact Moment Matching," Papers 1312.4443, arXiv.org.
    4. Dimitrakopoulos, Roussos G. & Abdel Sabour, Sabry A., 2007. "Evaluating mine plans under uncertainty: Can the real options make a difference?," Resources Policy, Elsevier, vol. 32(3), pages 116-125, September.
    5. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
    6. Jeroen Rombouts & Lars Peter Stentoft, 2010. "Multivariate Option Pricing With Time Varying Volatility and Correlations," CIRANO Working Papers 2010s-23, CIRANO.
    7. Axel Kind, 2005. "Pricing American-Style Options By Simulation," Financial Markets and Portfolio Management, Springer, vol. 19(1), pages 109-116, June.
    8. Georges Dionne & Geneviève Gauthier & Nadia Ouertani & Nabil Tahani, 2006. "Heterogeneous Basket Options Pricing Using Analytical Approximations," Cahiers de recherche 0605, CIRPEE.

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