Nonparametric Pricing of Multivariate Contingent Claims

FRB New York Working Paper No. 162

40 Pages Posted: 6 May 2003

Multiple version iconThere are 3 versions of this paper

Date Written: March 2003


Results from the method of copulas allow the multivariate risk-neutral density to be written as a product of marginal risk-neutral densities and a risk-neutral dependence function. A technique to price contingent claims can be developed using non-parametrically estimated marginal risk-neutral densities (based on options data) and a non-parametric dependence function (based on historical return data).

Non-parametric estimation eliminates the pricing biases that result from incorrect parametric assumptions such as lognormality. The technique generates fitted multivariate contingent claim prices that are consistent with prices of traded univariate options. Under some general conditions, the objective and risk-neutral dependence functions are identical, which justifies the use of historical return data for the non-parametric dependence function, so that no data are required on traded multivariate claims.

JEL Classification: C14, G13

Suggested Citation

Rosenberg, Joshua V., Nonparametric Pricing of Multivariate Contingent Claims (March 2003). FRB New York Working Paper No. 162, Available at SSRN: or

Joshua V. Rosenberg (Contact Author)

Independent ( email )

United States

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