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


  • Yacine Aït-Sahalia,

    1. University of Chicago and NBER
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  • Andrew W. Lo

    1. NBER and MIT
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    • * “Art-Sahalia is from the University of Chicago and the NBER, and Lo is from MIT and the NBER. We received helpful comments from George Constantinides, Eric Ghysels, Martin Haugh, John Heaton, Jens Jackwerth, Mark Rubinstein, René Stulz (the editor), Jiang Wang, two referees, and especially Lars Hansen, as well as seminar participants at Duke University, the Fields Institute, Harvard University, MIT, Tilburg University, the University of Chicago, ULB, Washington University, the Econometric Society Winter Meetings (1995), the NBER Asset Pricing Conference (1995), the NNCM Conference (1994) and the WFA Meetings (1996). A portion of this research was conducted during the first author's tenure as an IBM Corp. Faculty Research Fellow and the second author's tenure as an Alfred P. Sloan Research Fellow.


Implicit in the prices of traded financial assets are Arrow–Debreu prices or, with continuous states, the state-price density (SPD). We construct a nonparametric estimator for the SPD implicit in option prices and we derive its asymptotic sampling theory. This estimator provides an arbitrage-free method of pricing new, complex, or illiquid securities while capturing those features of the data that are most relevant from an asset-pricing perspective, for example, negative skewness and excess kurtosis for asset returns, and volatility “smiles” for option prices. We perform Monte Carlo experiments and extract the SPD from actual S&P 500 option prices.