State price density estimation via nonparametric mixtures

Details State price density estimation via nonparametric mixtures State price density estimation via nonparametric mixtures

2009-10-08

arxiv.org/abs/0910.1430v1

Annals of Applied Statistics 2009, Vol. 3, No. 3, 963-984

Economy

Quantitative Finance

Computational Finance

Published in at http://dx.doi.org/10.1214/09-AOAS246 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Ins

Scientific paper

10.1214/09-AOAS246

We consider nonparametric estimation of the state price density encapsulated in option prices. Unlike usual density estimation problems, we only observe option prices and their corresponding strike prices rather than samples from the state price density. We propose to model the state price density directly with a nonparametric mixture and estimate it using least squares. We show that although the minimization is taken over an infinitely dimensional function space, the minimizer always admits a finite dimensional representation and can be computed efficiently. We also prove that the proposed estimate of the state price density function converges to the truth at a ``nearly parametric'' rate.

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