New Book “Modern SABR Analytics” Authored by Numerix Focuses on How to Enhance the SABR Model for Better Derivatives Pricing

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24 June 2019

Numerix, the leader in risk technology, announces today the availability of Modern SABR Analytics, a new book published by Springer that explores accurate pricing of interest rate options. A team of financial quantitative experts including Michael Konikov, Senior Vice President of Quantitative Development, Numerix, Michael Spector, Vice President of Quantitative Research, Numerix, and former Numerix quant Alexandre Antonov, Director at Standard Chartered Bank and Risk’s 2016 Quant of the Year, focuses this new title on their advancement of an enhanced pricing and calibration capabilities under the SABR model.

“This team, comprised of current and former Numerix quantitative all-stars, is no stranger to collaboration, having joined forces previously to publish several articles that have appeared in Risk Magazine as Cutting Edge research,” said Serguei Issakov, Ph.D. Global Head of Quantitative Research & Senior Vice President, Quantitative Research Group at Numerix. “It is my belief that this new title will be of interest to experienced financial industry practitioners, as well as to mathematicians or students of mathematics who seek intuition in mathematical finance.”

Modern SABR Analytics: Formulas and Insights for Quants, Former Physicists and Mathematicians

The SABR model is a stochastic volatility model that is widely used to construct volatility cubes primarily for interest rate options. The option price is then computed—in an arbitrage-free way, in a theoretically consistent manner under the SABR model—based on the implied volatility. Theory versus practice, however, can often be miles apart and SABR is no exception.

While the model has proven to be a consistent solution for pricing options in an arbitrage-free way for positive rates, it has weakness as a tool for arbitrage-free pricing for very low or negative rates. Market participants would therefore have to resort to other means, such as extrapolation techniques or financial engineering tricks to try and fix this weakness. The authors, as is proven in the book, have discovered a natural way for SABR to accurately handle pricing in a low or negative rates environment.

Another solution presented in the book is an extension to SABR the authors came up with that they call Mixture SABR model, which makes SABR more flexible by making it possible to calibrate to swaption quotes and CMS quotes at the same time. Prior to this extension, SABR could not reproduce CMS quotes. This and other illuminating insights and formulas are included throughout the book, which is based on but not limited to the three papers that appeared in Risk Magazine:

  • - SABR Spreads its Wings: Provides accurate results on long maturity “wings” building on the proposed closed form solution for the zero-correlation case.
  • - The Free Boundary SABR: Natural Extension to Negative Rates: Adapts the popular SABR model to a negative rates environment.
  • - Mixing SABR Models for Negative Rates: Uses an exact formula for the normal free boundary SABR to construct an arbitrage-free mixed SABR with closed-form option prices and ability to jointly calibrate to swaptions and CMSs.

Order your copy of Modern SABR Analytics here:

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Banking, Corporate Banking
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Asia-Pacific, EMEA, LATAM, North America