Empirical pricing kernel estimation using a functional gradient descent algorithm based on splines

We propose a new methodology to estimate the empirical pricing kernel implied from option data. In contrast to most of the studies in the literature that use an indirect approach, i.e. first estimating the physical and risk-neutral densities and obtaining the pricing kernel in a second step, we follow a direct approach. Departing from an adequate parametric and economically motivated pricing kernel, we apply a functional gradient descent (FGD) algorithm based on B-splines. This approach allows us to locally modify the initial pricing kernel and hence to improve the final estimate. We empirically illustrate the estimation properties of the method and test its predictive power on S&P 500 option data, comparing it as well with other recent approaches introduced in the empirical pricing kernel literature.