Uniform Confidence Bands for Pricing Kernels

SFB 649 Discussion Paper 2010-003

30 Pages Posted: 9 Jan 2017

See all articles by Wolfgang K. Härdle

Wolfgang K. Härdle

Humboldt University of Berlin - Institute for Statistics and Econometrics; Xiamen University - Wang Yanan Institute for Studies in Economics (WISE); Charles University; Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Yarema Okhrin

University of Augsburg

Weining Wang

Humboldt University of Berlin

Date Written: January 7, 2010

Abstract

Pricing kernels implicit in option prices play a key role in assessing the risk aversion over equity returns. We deal with non-parametric 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 non-parametric regression. The subjective density is estimated non-parametrically 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, Non-parametric

JEL Classification: C00, C14, J01, J31

Suggested Citation

Härdle, Wolfgang K. and Okhrin, Yarema and Wang, Weining, Uniform Confidence Bands for Pricing Kernels (January 7, 2010). SFB 649 Discussion Paper 2010-003. Available at SSRN: https://ssrn.com/abstract=2894240 or http://dx.doi.org/10.2139/ssrn.2894240

Wolfgang K. Härdle (Contact Author)

Humboldt University of Berlin - Institute for Statistics and Econometrics ( email )

Unter den Linden 6
Berlin, D-10099
Germany

Xiamen University - Wang Yanan Institute for Studies in Economics (WISE) ( email )

A 307, Economics Building
Xiamen, Fujian 10246
China

Charles University ( email )

Celetná 13
Dept Math Physics
Praha 1, 116 36
Czech Republic

Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Unter den Linden 6
Berlin, D-10099
Germany

Yarema Okhrin

University of Augsburg ( email )

Universitätsstr. 2
Augsburg, 86159
Germany

Weining Wang

Humboldt University of Berlin ( email )

Unter den Linden 6
Berlin, AK Berlin 10099
Germany

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