Pricing individual stock options using both stock and market index information

When it comes to individual stock option pricing, most applications consider a univariate framework. From a theoretical point of view this is unsatisfactory as we know that the expected return of any asset is closely related to the exposure to the market risk factors. To address this, we model the evolution of the individual stock returns together with the market index returns in a flexible bivariate model in line with theory. The model parameters are estimated using both historical returns and aggregated option data from the index and the individual stocks. We assess the model performance by pricing a large set of individual stock options on 26 major US stocks over a long time period including the global financial crisis. Our results show that the losses from using a univariate formulation amounts to 11% on average when compared to our preferred bivariate specification.