Nonparametric option pricing under shape restrictions

Yacine Aït-Sahalia, Jefferson Duarte

Research output: Contribution to journalArticlepeer-review

173 Scopus citations


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&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.

Original languageEnglish (US)
Pages (from-to)9-47
Number of pages39
JournalJournal of Econometrics
Issue number1-2
StatePublished - Sep 2003

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics


  • Constraints
  • Convexity
  • Kernel
  • Local polynomials
  • Monotonicity
  • Regression
  • State price density


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