A new bivariate approach for modeling the interaction between stock volatility and interest rate: An application to S&P500 returns and options

The GARCH models developed so far do not take into account the interaction between the volatility of asset returns and the dynamics of the interest rate. In this paper, we propose a bivariate GARCH model in which interest rate movements and asset price volatility are fully coupled. This approach yields explicit and simple to implement recursion formulas for the moment generating function, which can be exploited to compute option prices by applying the fast Fourier transform or other convolution techniques. We perform a thorough and comprehensive empirical analysis based on real S&P500 return and option data showing the usefulness and robustness of the suggested methodology. Both in-sample and out-of-sample results reveal the superiority of our approach over the GARCH model with constant interest rates.