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Estimation of risk-neutral measures using quartic B-spline cumulative distribution functions with power tails

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  • Seung Hwan Lee

Abstract

In this paper, we propose the B-spline (BSP) method, which overcomes problems with the smoothed implied volatility smile (SML) method for estimating option implied risk-neutral measures (RNMs). We model the risk-neutral cumulative distribution function (CDF) using quartic B-splines with power tails so that the resulting risk-neutral probability density function (PDF) has continuity and arbitrage-free properties. Since the number of knots is selected optimally in constructing the quartic B-spline risk-neutral CDF, our method avoids both overfitting and oversmoothing. To improve computational efficiency and accuracy, we introduce a three-step RNM estimation procedure that transforms a nonlinear optimization problem into a convex quadratic program. Monte-Carlo experiments and applications to S&P 500 index options suggest that the BSP method performs considerably better than the SML method. The BSP method always produces arbitrage-free RNM estimators and almost perfectly recovers the actual risk-neutral PDFs for various hypothetical distributions.

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  • Seung Hwan Lee, 2014. "Estimation of risk-neutral measures using quartic B-spline cumulative distribution functions with power tails," Quantitative Finance, Taylor & Francis Journals, vol. 14(10), pages 1857-1879, October.
    • Handle: RePEc:taf:quantf:v:14:y:2014:i:10:p:1857-1879
    DOI: 10.1080/14697688.2012.742202
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    3. Liyuan Jiang & Shuang Zhou & Keren Li & Fangfang Wang & Jie Yang, 2018. "A New Nonparametric Estimate of the Risk-Neutral Density with Applications to Variance Swaps," Papers 1808.05289, arXiv.org, revised Feb 2019.

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