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The Journal of Derivatives

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Universal Arbitrage-Free Estimation of State Price Density

Qi Hu and David Newton
The Journal of Derivatives Spring 2021, jod.2020.1.123; DOI: https://doi.org/10.3905/jod.2020.1.123
Qi Hu
is now a quant researcher with Deep Sea Lab, Tencent, China
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David Newton
is a professor at the School of Management at the University of Bath in Bath, United Kingdom
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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.

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The Journal of Derivatives: 29 (5)
The Journal of Derivatives
Vol. 29, Issue 5
Summer 2022
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Universal Arbitrage-Free Estimation of State Price Density
Qi Hu, David Newton
The Journal of Derivatives Nov 2020, jod.2020.1.123; DOI: 10.3905/jod.2020.1.123

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Universal Arbitrage-Free Estimation of State Price Density
Qi Hu, David Newton
The Journal of Derivatives Nov 2020, jod.2020.1.123; DOI: 10.3905/jod.2020.1.123
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  • Article
    • Abstract
    • SPD AND OPTION PRICES
    • SUPPORT VECTOR MACHINE FRAMEWORK
    • EMPIRICAL ANALYSIS
    • COMPARISON OF NONPARAMETRIC METHODS
    • CONCLUSION
    • APPENDIX A
    • APPENDIX B
    • APPENDIX C
    • ENDNOTES
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