Universal Arbitrage-free Estimation of State Price Density

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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.
Original languageEnglish
Pages (from-to)35-59
Number of pages25
JournalJournal of Derivatives
Issue number3
Early online date21 Nov 2020
Publication statusPublished - 1 Mar 2021


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


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