TY  - JOUR
AU  - Ait-Sahalia,Yacine
AU  - Duarte,Jefferson
TI  - Nonparametric Option Pricing under Shape Restrictions
JF  - National Bureau of Economic Research Working Paper Series
VL  - No. 8944
PY  - 2002
Y2  - May 2002
UR  - http://www.nber.org/papers/w8944
L1  - http://www.nber.org/papers/w8944.pdf
N1  - Author contact info:
Yacine Ait-Sahalia
Department of Economics
Fisher Hall
Princeton University
Princeton, NJ 08544-1021
Tel: 609/258-4015
Fax: 609/258-0719
E-Mail: yacine@princeton.edu

Jefferson Duarte
University of Washington
E-Mail: jduarte@u.washington.edu
AB  - 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.
ER  -