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Nonparametric Option Pricing under Shape Restrictions

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  • Yacine Ait-Sahalia
  • 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.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 8944.

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Date of creation: May 2002
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Publication status: published as Journal of Econometrics, 2003, vol. 116, pp. 9-47
Handle: RePEc:nbr:nberwo:8944

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