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Though the recent announcements by the Bank of Hungary and the Bank of Japan to adopt negative interest rates took much of the world by surprise, these weren't especially remarkable to European derivative practitioners. By now negative interest rates have become somewhat common place, with the Euro Zone in particular experiencing first hand their impacts for more than a year and a half following European Central Bank's lead in moving below zero.
Their growing presence is however somewhat remarkable when just five years ago the concept of a negative interest rate was so implausible that most derivative pricing models were designed to work exclusively with positive rates. This new negative rate environment brings forth two prominent resulting challenges – the quotation of option volatilities and volatility smile interpolation models, such as SABR.
In his “revolutionary” research, Dr. Alexander Antonov, SVP of Quantitative Research at Numerix, took on this challenge, proposing to go beyond the crude-fix practice of a shifted SABR, to devise a solution that no longer required recalibration each time rates became too negative. This Free Boundary SABR approach helped to earn him the honor of Risk Magazine's Quant of the Year 2016.
On April 28, 2016, Dr. Antonov gave a lecture delving into the issue of negative interest rates in light of the recent BOJ announcement, his Free Boundary SABR approach and how financial software must adjust for these new challenges.
Dr. Antonov addressed:
- Negative rates review
- Adapting financial software to negative rates: challenges
- Volatility quotation: from Black to Bacheleir
- Swaption cube construction-- modifying the SABR:
- Beyond the simple shifted SABR
- Free Boundary SABR (Exact analytical solution for zero correlation; Accurate approximation for the general correlation)
- Normal Free SABR (Exact analytical solution for general correlation)
- New Mixture SABR (Mixing zero correlation Free SABR with the normal Free one; Arbitrage free analytical solution via 1D integral)
- Numerical results and conclusion (Joint calibration to swaptions and CMS’s; Comparison of the Shifted, Free and Mixture SABR: the clear winner is the mixture SABR)
- Term structure interest rate models suitable for negative rates
- Discussion and conclusions
Attendance is complimentary, but registration is required.
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Alexandre Antonov, PhD, Senior Vice President of Quantitative Research, Numerix
Dr. Antonov holds the honor of Risk Magazine’s 2016 Quant of the Year. He first began studying Physics and Mathematics at the Moscow Institute of Physics and Technology, followed by the Landau Institute for Theoretical Physics (PhD in 1997) and The Laboratory of Theoretical and High Energy Physics at the University of Paris VI. In March 1998 Alexandre he joined Numerix based in Paris taking on a number of positions during his tenure with the company including Quantitative Analyst, Senior Quantitative Analyst, Vice President and Senior Vice President. During the course of his career Dr. Antonov has had over twenty articles published in industry journals, including six that have appeared on the pages of Risk Magazine.