European Options Sensitivity with Respect to the Correlation for Multidimensional Heston Models

Abstract

International audienceThis paper is devoted to the sensitivity study of the European option prices according to the correlation parameters when dealing with the multi-asset Heston model. When the Feller condition is not fulfilled, the CIR flow regularity is needed to prove the differentiability of the price according to the correlation. In the bidimensional case when the Feller condition is satisfied, the regularity of the volatility according to the correlation allows us to establish an asymptotic expression of the derivative of the price with respect to the correlation. This approximation provides the monotony for the exchange options then heuristically for spread option prices at short maturities. We also obtain this monotony for some restrictive choices of the products $\{ \eta_i \rho_i \}_{i=1,2}$ and $\{ \eta_i \sqrt{1-\rho_i^2} \}_{i=1,2}$ where $\eta_i$ is the volatility of the volatility and $\rho_i$ is the asset/volatility correlation coefficient. Then, we explain how to extend the overall study to options written on more than two assets and on models that are derived from Heston model, like the double Heston model. We conclude by a large number of simulations that comfort the theoretical results