Nonparametric estimation of state-price densities implicit in financial asset prices

An estimator is constructed for the SPD implicit in financial asset prices and an asymptotic sampling theory is derived for this estimator to gauge its accuracy.

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) that may be used to price all assets, traded or non-traded. Using recently developed techniques in nonparametric analysis, we construct an estimator for the SPD implicit in financial asset prices and we derive an asymptotic sampling theory for this estimator to gauge its accuracy. We perform Monte Carlo simulation experiments to see whether the SPD estimator can be used successfully to price and hedge derivative securities, and we also provide several illustrative empirical examples using both hypothetical and actual options prices on S&P 500 index options.