The shape of small sample biases in pricing kernel estimations

Dietmar P. J. Leisen

Quantitative Finance, 2017, vol. 17, issue 6, 943-958

Abstract: 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 the first step, we analyse theoretically the functional dependence for the ratio of a density to its estimated density; this cautions the reader regarding potential computational issues coupled with statistical techniques. In the 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 centre even when the true pricing kernel fulfils these. This contributes to an alternative, statistical explanation for the puzzling shape in pricing kernel estimations.

Date: 2017
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DOI: 10.1080/14697688.2016.1258486

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