EUROPEAN OPTIONS SENSITIVITY WITH RESPECT TO THE CORRELATION FOR MULTIDIMENSIONAL HESTON MODELS

We study the sensitivity of European option prices with respect to correlation parameters in the multi-asset Heston model. The differentiability of the price function with respect to the correlation is proved by using the regularity of the flow of the Cox–Ingersoll–Ross model. In the bidimensional case and when the Feller condition is satisfied, we establish an asymptotic approximation for the derivative of the price with respect to the correlation for short maturities. This approximation is used to discuss monotony issues for exchange and spread option prices. Monotony properties are also obtained for some values of "the volatility of the volatility parameter" and of the correlation between stock prices and their volatilities. We conclude with a large number of simulations that confirm the theoretical results.