Uniform confidence bands for pricing kernels

Wolfgang Karl Härdle, Yarema Okhrin and Weining Wang

No SFB649DP2010-003, SFB 649 Discussion Papers from Humboldt University, Collaborative Research Center 649

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 (Empirical Pricing Kernel) given by the ratio of the risk-neutral density estimator and the subjective density estimator. 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. The subjective density is estimated nonparametrically too. In this framework, we develop the asymptotic distribution theory of the EPK in the L1 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 (search for similar items in EconPapers)
JEL-codes: C00 C14 J01 J31 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2010-01
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