Generalizing the Black-Scholes Formula to Multivariate Contingent Claims

Posted: 10 May 2006

See all articles by Rene Carmona

Rene Carmona

Princeton University - Bendheim Center for Finance

Valdo Durrelman

Stanford University

Abstract

This paper provides approximate formulas that generalize the Black-Scholes formula in all dimensions. Pricing and hedging of multivariate contingent claims are achieved by computing lower and upper bounds. These bounds are given in closed form in the same spirit as the classical one dimensional Black-Scholes formula. Lower bounds perform remarkably well. Similar to the one-dimensional case, Greeks are also available in closed form. We discuss an extension to basket options with barrier.

Keywords: Black-Scholes, pricing, hedging, lower bonds, upper bonds, Greeks, basket options, barrier

Suggested Citation

Carmona, Rene and Durrelman, Valdo, Generalizing the Black-Scholes Formula to Multivariate Contingent Claims. Journal of Computational Finance, Vol. 9, No. 2, Spring 2006, Available at SSRN: https://ssrn.com/abstract=900310

Rene Carmona (Contact Author)

Princeton University - Bendheim Center for Finance ( email )

26 Prospect Avenue
Princeton, NJ 08540
United States

Valdo Durrelman

Stanford University ( email )

Stanford, CA 94305
United States

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