Estimation of risk-neutral measures using quartic B-spline cumulative distribution functions with power tails
Seung Hwan Lee
Quantitative Finance, 2014, vol. 14, issue 10, 1857-1879
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.
References: View references in EconPapers View complete reference list from CitEc
Citations View citations in EconPapers (1) Track citations by RSS feed
Downloads: (external link)
Access to full text is restricted to subscribers.
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:taf:quantf:v:14:y:2014:i:10:p:1857-1879
Ordering information: This journal article can be ordered from
Access Statistics for this article
Quantitative Finance is currently edited by Michael Dempster and Jim Gatheral
More articles in Quantitative Finance from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().