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

51 Pages Posted: 20 Jul 2000 Last revised: 17 Aug 2022

See all articles by Yacine Ait-Sahalia

Yacine Ait-Sahalia

Princeton University - Department of Economics

Andrew W. Lo

Massachusetts Institute of Technology (MIT) - Laboratory for Financial Engineering

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Date Written: November 1995

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.

Suggested Citation

Ait-Sahalia, Yacine and Lo, Andrew W., Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices (November 1995). NBER Working Paper No. w5351, Available at SSRN: https://ssrn.com/abstract=225414

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