Bivariate option pricing using dynamic copula models

Abstract

This paper examines the behavior of bivariate option prices in the presence of association between the underlying assets. Parametric families of copulas offering various alternatives to the Gaussian dependence structure are used to model this association, which is explicitly assumed to vary over time as a function of the volatilities of the assets. These dynamic copula models are applied to better-of-two-markets and worse-of-two-markets options on the Standard and Poor’s 500 and Nasdaq indexes. Results show that option prices implied by dynamic copula models can differ substantially from prices implied by models that fix the dependence between the underlyings, particularly in times of high volatilities. In the study, the Gaussian copula also produced option prices that differed significantly from those induced by non-Gaussian copulas, irrespective of initial volatility levels. Within the class of alternatives considered, option prices were robust with respect to the choice of copula.