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September 2009 State price density estimation via nonparametric mixtures
Ming Yuan
Ann. Appl. Stat. 3(3): 963-984 (September 2009). DOI: 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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Ming Yuan. "State price density estimation via nonparametric mixtures." Ann. Appl. Stat. 3 (3) 963 - 984, September 2009.


Published: September 2009
First available in Project Euclid: 5 October 2009

zbMATH: 1196.62134
MathSciNet: MR2750382
Digital Object Identifier: 10.1214/09-AOAS246

Keywords: Black–Scholes equation , European call options , nonparametric mixture , state price density

Rights: Copyright © 2009 Institute of Mathematical Statistics


Vol.3 • No. 3 • September 2009
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