Nonparametric Estimation of State-Price Densities Implicit In Financial Asset Prices

Yacine Aït-Sahalia
Graduate School of Business, The University of Chicago
Yacine.Aitsahalia@gsbsun.uchicago.edu

Andrew W. Lo
Sloan School of Management, MIT and NBER

Abstract

Implicit in the prices of traded financial assets are Arrow-Debreu state prices or, in the continuous-state case, the state-price density (SPD). We construct an estimator for the SPD implicit in option prices and derive an asymptotic sampling theory for this estimator to gauge its accuracy. The SPD estimator provides an arbitrage-free method of pricing new, more complex, or less liquid securities while capturing those features of the data that are most relevant from an asset-pricing perspective, e.g., negative skewness and excess kurtosis for asset returns, volatility ``smiles'' for option prices. We perform Monte Carlo simulation experiments to show that the SPD estimator can be successfully extracted from option prices and we present an empirical application using S&P 500 index options.