Estimation of Risk-Neutral Densities Using Positive Convolution Approximation

27 Pages Posted: 17 Feb 2003 Last revised: 14 Oct 2014

See all articles by Oleg Bondarenko

Oleg Bondarenko

University of Illinois at Chicago - Department of Finance

Date Written: August 1, 2002

Abstract

This paper proposes a new nonparametric method for estimating the conditional risk-neutral density (RND) from a cross-section of option prices. The idea of the method is to fit option prices by finding the optimal density in a special admissible set. The admissible set consists of functions, each of which may be represented as a convolution of a positive kernel with another density. The method is termed the Positive Convolution Approximation (PCA). The important properties of PCA are that it 1) is completely agnostic about the data generating process, 2) controls against overfitting while allowing for small samples, 3) always produces arbitrage-free estimators, and 4) is computationally simple. In a Monte-Carlo experiment, PCA is compared to several popular methods: mixtures of lognormals (with one, two, and three lognormals), Hermite polynomials, two regularization methods (for the RND and for implied volatilities), and sigma shape polynomials. PCA is found to be a promising alternative to the competitors.

JEL Classification: C13, C14, G13

Suggested Citation

Bondarenko, Oleg, Estimation of Risk-Neutral Densities Using Positive Convolution Approximation (August 1, 2002). Journal of Econometrics, Vol. 116, pp. 85-112, 2003. Available at SSRN: https://ssrn.com/abstract=375781 or http://dx.doi.org/10.2139/ssrn.375781

Oleg Bondarenko (Contact Author)

University of Illinois at Chicago - Department of Finance ( email )

2431 University Hall (UH)
601 S. Morgan Street
Chicago, IL 60607-7124
United States
(312) 996-2362 (Phone)
(312) 413-7948 (Fax)

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