Leitura do Dia - Nonparametric option pricing under shape restrictions

A leitura do dia de hoje é um dos meus artigos favoritos em finanças. A motivação é intuitiva, os resultados são úteis e gerou toda uma linha de pesquisa.


Nonparametric option pricing under shape restrictions
Yacine Ait-Sahalia, Jeferson Duarte
aDepartment of Economics, Princeton University and NBER, Princeton, NJ 08544-1021, USA
bDepartment of Finance and Business Economics, University of Washington, 267 MacKenzie Hall,
Box 353200, Seattle, WA 98195-3200, USA

Abstract
Frequently, economic theory places shape restrictions on functional relationships between economic variables. This paper develops a method to constrain the values of the 2rst 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&P 500 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: State price density; Kernel; Local polynomials; Regression; Constraints; Monotonicity; Convexity