Working Paper: NBER ID: w8944
Authors: Yacine Aitsahalia; Jefferson Duarte
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.
Keywords: nonparametric estimation; option pricing; shape restrictions; state price density
JEL Codes: G12; C14
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| absence of arbitrage opportunities (G19) | pricing operator is linear (D41) |
| imposing shape restrictions (C24) | accuracy of nonparametric estimators (C14) |
| monotonicity and convexity constraints (C61) | estimated state price density (SPD) remains valid (C13) |
| constrained estimators (C51) | more accurate results (C52) |
| first and second derivatives satisfy inequality constraints (C61) | prevent violations of the no-arbitrage principle (G19) |
| unconstrained nonparametric estimators violate constraints (C51) | reliability of the estimators (C51) |