When it comes to individual stock option pricing, most, if not all, applications consider a univariate framework in which the dynamics of the underlying asset is considered without taking the evolution of the market or any other risk factors into consideration. From a theoretical point of view this is clearly unsatisfactory as we know, i.e. from the Capital Asset Pricing Model, that the expected return of any asset is closely related to the exposure to the market risk factor. On top of this theoretical inconsistency in empirical applications it is often difficult to precisely assess and appropriately measure risk premia from individual stock returns alone. To address these shortcomings, we model the evolution of the individual stock returns together with the market index returns in a bivariate model that allows us to estimate risk premia in line with the theory. We assess the performance of the model by pricing individual stock options on the constituent stocks in the Dow Jones Industrial Average over a long time period including the recent Global Financial Crisis.