Abstract

https://ssrn.com/abstract=2894237
 


 



Nonparametric Estimation of Risk-Neutral Densities


Maria Grith


Humboldt University of Berlin

Wolfgang K. Härdle


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

Melanie Schienle


Karlsruhe Institute of Technology (KIT)

April 1, 2010

SFB 649 Discussion Paper 2010-021

Abstract:     
This chapter deals with nonparametric estimation of the risk neutral density. We present three different approaches which do not require parametric functional assumptions on the underlying asset price dynamics nor on the distributional form of the risk neutral density. The first estimator is a kernel smoother of the second derivative of call prices, while the second procedure applies kernel type smoothing in the implied volatility domain. In the conceptually different third approach we assume the existence of a stochastic discount factor (pricing kernel) which establishes the risk neutral density conditional on the physical measure of the underlying asset. Via direct series type estimation of the pricing kernel we can derive an estimate of the risk neutral density by solving a constrained optimization problem. The methods are compared using European call option prices. The focus of the presentation is on practical aspects such as appropriate choice of smoothing parameters in order to facilitate the application of the techniques.

Number of Pages in PDF File: 31

Keywords: Risk neutral density, Pricing kernel, Kernel smoothing, Local polynomials, Series methods

JEL Classification: C13, C14, G12


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Date posted: January 10, 2017  

Suggested Citation

Grith, Maria and Härdle, Wolfgang K. and Schienle, Melanie, Nonparametric Estimation of Risk-Neutral Densities (April 1, 2010). SFB 649 Discussion Paper 2010-021. Available at SSRN: https://ssrn.com/abstract=2894237

Contact Information

Maria Grith
Humboldt University of Berlin ( email )
Unter den Linden 6
Berlin, Berlin 10099
Germany
Wolfgang K. Härdle (Contact Author)
Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)
Unter den Linden 6
Berlin, D-10099
Germany
Humboldt University of Berlin - Institute for Statistics and Econometrics ( email )
Unter den Linden 6
Berlin, D-10099
Germany
+49 30 2093 5631 (Phone)
+49 30 2093 5649 (Fax)
Melanie Schienle
Karlsruhe Institute of Technology (KIT) ( email )
Institute of Economics (ECON)
Karlsruhe
Germany
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