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 nontrivial task because of data limitation and the complex arbitrage-free constraints. In this article, we develop a more effective linear programming support vector machine 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.

TOPICS: Derivatives, options

Key Findings

• ▪ Recovery of a well-behaved state price density is an important but nontrivial because of data limitation and the complex arbitrage-free constraints.

• ▪ We develop a universally applicable linear programming support vector machine estimator for state price density that incorporates no-arbitrage restrictions and bid-ask spread.

• ▪ We apply the method empirically to options on the S&P 500, showing it to be accurate and smooth.