NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

Nonparametric Option Pricing under Shape Restrictions

Yacine Ait-Sahalia, Jefferson Duarte

NBER Working Paper No. 8944
Issued in May 2002
NBER Program(s):   AP

Frequently, economic theory places shape restrictions on functional relationships between economic variables. This paper develops a method to constrain the values of the first and second derivatives of nonparametric locally polynomial estimators. We apply this technique to estimate the state price density (SPD), or risk-neutral density, implicit in the market prices of options. The option pricing function must be monotonic and convex. Simulations demonstrate that nonparametric estimates can be quite feasible in the small samples relevant for day-to-day option pricing, once appropriate theory-motivated shape restrictions are imposed. Using S&P500 option prices, we show that unconstrained nonparametric estimators violate the constraints during more than half the trading days in 1999, unlike the constrained estimator we propose.

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Document Object Identifier (DOI): 10.3386/w8944

Published: Journal of Econometrics, 2003, vol. 116, pp. 9-47 citation courtesy of

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