Universal Arbitrage-Free Estimation of State Price Density

Abstract

Given the valuable information content of Arrow-Debreu prices, the recovery of a well behaved state price density is of considerable importance. However, this is a non-trivial task due to data limitation and the complex arbitrage-free constraints. In this paper, we develop a more effective linear programming support vector machine (SVM) estimator for state price density which incorporates no-arbitrage restrictions and bid-ask spread. This method does not depend on a particular approximation function and framework and is, therefore, universally applicable.In a parallel empirical study, we apply the method to options on the S&P 500, showing it to be accurate and smooth.