Nonparametric Option Pricing under Shape Restrictions

Yacine Ait-Sahalia and Jefferson Duarte

No 8944, NBER Working Papers from National Bureau of Economic Research, Inc

Abstract: 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.

JEL-codes: C14 G12 (search for similar items in EconPapers)
Date: 2002-05
New Economics Papers: this item is included in nep-fin and nep-fmk
Note: AP
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Citations: View citations in EconPapers (3)

Published as Journal of Econometrics, 2003, vol. 116, pp. 9-47

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Journal Article: Nonparametric option pricing under shape restrictions (2003)
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