Multivariate asset price dynamics with stochastic covariation

Abstract

Stochastic volatility models such as those of Heston [Rev. Financial Stud., 1993, 6(2), 327–343] and Hull and White [J. Finance, 1987, 42(2), 281–300] are often used to model volatility risk in the pricing and hedging of contingent claims on risky assets. Recent empirical evidence has shown that these models under general specifications often do not fully capture the volatility dynamics observed in situ. This paper provides an analytical demonstration of the consequences of multivariate stochastic covariation on the pricing of contingent claims and suggests a hedging strategy for full delta neutrality.