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Negative interest rates are becoming increasingly common around the globe, with the Euro Zone in particular experiencing firsthand the impact of negative rates for more than a year and a half, following the European Central Bank's lead in moving rates below zero. The Netherlands and Finland, as part of the Euro Zone, have experienced aggressive rate cuts by the ECB resulting in the yield curve in negative territory up to 7 years maturity—with the shortest maturities (below 2 years) becoming negative in excess of 45 basis points. In other Nordic countries, like Denmark and Sweden, we see negative interest rates up to 5 years maturity. In the meantime, Norway has low, but positive interest rates across the yield curve.

The growing presence of negative interest rates is remarkable—when just five years ago the concept of negative interest rates 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 Wednesday June 8, 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
    • HW model
    • Shifted LMM
  • Discussion and conclusions
Attendance is complimentary, but registration is required.
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Alexander Antonov, PhD, Senior Vice President of Quantitative Research, Numerix

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.

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Resources for Navigating Negative Rates