Multivariate asset price dynamics with stochastic covariation

Stochastic volatility models such as those of Heston [Rev. Financial Stud., 1993 Heston, SL. 1993. A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financial Stud., 6(2): 327–343. and Hull and White J. Finance, 1987 Hull, JC and White, AD. 1987. The pricing of options on assets with stochastic volatilities. J. Finance, 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.