Multivariate Option Pricing Using Dynamic Copula Models

Abstract

This paper examines the behavior of multivariate option prices in the presence of association between the underlying assets. Parametric families of copulas offering various alternatives to the normal 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 S&P500 and Nasdaq indexes. Results show that option prices implied by dynamic copula models differ substantially from prices implied by models that fix the dependence between the underlyings, particularly in times of high volatilities. Furthermore, the normal copula produces option prices that differ significantly from non-normal copula prices, irrespective of initial volatility levels. Within the class of non-normal copula families considered, option prices are robust with respect to the copula choice.