# American Institute of Mathematical Sciences

October  2015, 11(4): 1185-1209. doi: 10.3934/jimo.2015.11.1185

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

 1 BBVA and University Institute for Economic and Social Analysis, University of Alcalá, Mailing address: c/ Sauceda, 28 Edicio ASIA, 28050, Madrid, Spain

Received  January 2014 Revised  September 2014 Published  March 2015

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.
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.
Citation: Jacinto Marabel Romo. A closed-form solution for outperformance options with stochastic correlation and stochastic volatility. Journal of Industrial & Management Optimization, 2015, 11 (4) : 1185-1209. doi: 10.3934/jimo.2015.11.1185
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