Empirical Asset Pricing with Functional Factors

We propose a methodology to use functional factors in empirical asset pricing models. We establish conditions under which it is possible to recover linear beta pricing. The proposed estimation approach allows us to use high-dimensional functional curves, such as the term structure of interest rates or the implied volatility smile, as factors. This framework enables the estimation of functional factor loadings as well as risk premium parameters of factor models. We derive estimation algorithms and establish the asymptotic consistency and normality of the parameter estimates. In an empirical application, we show that the implied variance smile of the S&P500 is a potential pricing factor for momentum-sorted portfolios. In particular, a positive risk premium is earned by the convexity of the implied variance curve.