Abstract
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.
Highlights
In recent years there has been a remarkable growth of multi-asset options
This article introduces a multi-asset model based on Wishart processes that accounts for stochastic volatility and for stochastic correlation between the underlying assets, as well as between their volatilities
The growth experienced in recent years in both the variety and volume of structured products with embedded multi-asset options, which are trade in the over-the-counter market, implies that banks and other financial institutions have become increasingly exposed to correlation between the underlying assets
Summary
In recent years there has been a remarkable growth of multi-asset options. These options exhibit sensitivity to the volatility of the underlying assets, as well as to their correlations. The comparison of the prices obtained under a multi-asset local volatility model and under a multi-asset version of the Heston (1993) stochastic volatility model with constant instantaneous correlations, shows that these models are not flexible enough to capture the sensitivity of the outperformance option with respect to the term structure of correlation and, are not able to yield the same price for this option that the model presented in this article. The features of the model presented in this article make it suitable for pricing other multi-asset options such as best-of or worst-of options which are quite sensitive to the evolution of the correlation corresponding to the underlying assets returns, as well as to the evolution of their instantaneous volatilities.
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