A closed-form solution for outperformance options with stochastic correlation and stochastic volatility

Outperformance options allow investors to benefit from a view on the relative performance of two underlying assets without taking any directional exposure to the evolution of the market. These structures exhibit high sensitivity to the correlation between the underlying assets and are usually priced assuming constant instantaneous correlations. &nbsp This article considers a multi-asset model based on Wishart processes that accounts for stochastic volatility and for stochastic correlations between the assets returns, as well as between their volatilities. Under the assumptions of the model this article provides semi-closed form solutions for the price of outperformance options. The article shows that the price of these options depends crucially on the term structure of the correlation corresponding to the assets returns. Furthermore, the comparison of the prices obtained under this model and under other models with constant correlations commonly used by financial institutions reveals the existence of a stochastic correlation premium.