Estimation Of Excess Returns From Derivative Prices And Testing For Risk Neutral Pricing

This paper develops an econometric framework for (i) estimating excess returns of the security process from high frequency derivative prices, (ii) testing for risk neutral pricing, and (iii) measuring premiums outside the no-arbitrage pricing model. The estimator is constructed by applying quasi-likelihood and Feynman–Kac theory to the risk neutral contingent claims pricing model to generate the optimal orthogonality restriction. The strong consistency and asymptotic normality of the estimator are established in the context of a nonstationary underlying state process. These results further imply that the estimator is robust to distributional assumptions on the underlying asset process. The proposed approach is applicable to any arbitrary derivative security, does not require estimation of the risk neutral probability measure, and has application to spot rate bond pricing models. A controlled diagnostic study based on generating the S&P500 index and calls verifies the ability of the estimators to correctly estimate security excess returns and test for risk neutral pricing. The estimator is invariant to call strikes, and larger samples constructed by cycling over shorter maturity options can be used to reduce its variance.