The Shape of Small Sample Biases in Pricing Kernel Estimations
34 Pages Posted: 17 Mar 2014 Last revised: 22 Sep 2016
Date Written: September 20, 2016
Numerous empirical studies find pricing kernels that are not-monotonically decreasing; the findings are at odds with the pricing kernel being marginal utility of a risk-averse, so-called representative agent. We study in detail the common procedure which estimates the pricing kernel as the ratio of two separate density estimations. In a first step, we analyze theoretically the functional dependence for the ratio of a density to its estimated density; this cautions the reader of potential computational issues coupled with statistical techniques. In a second step, we study this quantitatively; we show that small sample biases shape the estimated pricing kernel, and that estimated pricing kernels typically violate the commonly believed monotonicity at the center even when the true pricing kernel fulfills these. This contributes to alternative, statistical explanations for the puzzling shape in pricing kernel estimations.
Keywords: small sample bias, pricing kernel puzzle, implied volatility, kernel density estimation
JEL Classification: G12, C14, C22, C58
Suggested Citation: Suggested Citation