Universal Arbitrage-free Estimation of State Price Density

David Newton, Qi Hu

OAI: oai:purehost.bath.ac.uk:publications/9a6cc4f6-ff45-45fe-a63d-ddb19c1ff05a • DOI: https://doi.org/10.3905/jod.2020.1.123

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 e˙ective 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.

State price density Non-parametric estimation No-arbitrage constraints Support vector machine regression