Uniform Confidence Bands for Pricing Kernels

Wolfgang Härdle, Yarema Okhrin and Weining Wang

Journal of Financial Econometrics, 2015, vol. 13, issue 2, 376-413

Abstract: Pricing kernels implicit in option prices play a key role in assessing the risk aversion over equity returns. We deal with nonparametric estimation of the pricing kernel (PK) given by the ratio of the risk-neutral density estimator and the historical density (HD). The former density can be represented as the second derivative w.r.t. the European call option price function, which we estimate by nonparametric regression. HD is estimated nonparametrically too. In this framework, we develop the asymptotic distribution theory of the Empirical Pricing Kernel (EPK) in the L∞ sense. Particularly, to evaluate the overall variation of the pricing kernel, we develop a uniform confidence band of the EPK. Furthermore, as an alternative to the asymptotic approach, we propose a bootstrap confidence band. The developed theory is helpful for testing parametric specifications of pricing kernels and has a direct extension to estimating risk aversion patterns. The established results are assessed and compared in a Monte-Carlo study. As a real application, we test risk aversion over time induced by the EPK.

Keywords: empirical pricing kernel; confidence band; bootstrap; kernel smoothing; nonparametric fitting (search for similar items in EconPapers)
JEL-codes: C14 J01 J31 (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Working Paper: Uniform confidence bands for pricing kernels (2010)
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