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Journal of Financial Econometrics Advance Access originally published online on November 7, 2008
Journal of Financial Econometrics 2009 7(2):53-76; doi:10.1093/jjfinec/nbn016
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Nonparametric Option Pricing with No-Arbitrage Constraints

Melanie Birke
     Ruhr-Universität Bochum

Kay F. Pilz
     Sal. Oppenheim jr. & Cie. KGaA

Address correspondance to Melanie Birke, Ruhr-Universität Bochum, Fakultät für Mathematik, Universitätsstr. 150, 44780 Bochum, Germany, or e-mail: melanie.birke{at}rub.de.

JEL Classification: C14, G12


  Abstract

We propose a completely kernel based method of estimating the call price function or the state price density of options. The new estimator of the call price function fulfills the constraints like monotonicity and convexity given in Breeden and Litzenberger (1978) without necessarily estimating the state price density for an underlying asset price from its option prices. It can be shown that the call price estimator is pointwise consistent and asymptotically normal. The estimator of the state price density is also consistent. In a simulation study we compare the new estimators to the estimators given in Aït-Sahalia and Duarte (2003).

KEYWORDS: call pricing function, constrained nonparametric estimation, monotone rearrangements, state price density

The authors are grateful to H. Dette for his helpful comments on this topic. We also would like to thank Y. Aït-Sahalia for some helpful hints concerning their paper and the simulations. The work of one of the authors was supported by the Sonderforschungsbereich 475, Komplexitätsreduktion in multivariaten Datenstrukturen. This work reflects the views of the author only, not those of Sal. Oppenheim.

Received July 10, 2007; revised August 18, 2008; accepted September 24, 2008


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