The Dynamic Correlation Model and Its Application to the Heston Model

Abstract

Correlation plays an essential role in many problems of finance and economics, such as pricing financial products and hedging strategies, since it models the degree of relationship between, e.g., financial products and financial institutions. However, usually for simplicity the correlation coefficient is assumed to be a constant in many models, although financial quantities are correlated in a strongly nonlinear way in the real market. This work provides a new time-dependent correlation function, which can be easily used to construct dynamically (time-dependent) correlated Brownian motions and flexibly incorporated in many financial models. The aim of using our time-dependent correlation function is to reasonably choose additional parameters to increase the fitting quality on the one hand, but also add an economic concept on the other hand. As examples, we illustrate the applications of dynamic correlation in the Heston model. From our numerical results we conclude that the Heston model extended by incorporating time-dependent correlations can provide a better volatility smile than the pure Heston model.