A new arbitrage-free parametric volatility surface

Michael Konikov and Michael Spector of Numerix jointly with Alexandre Antonov at Danske Bank describe a new parametric volatility surface that is arbitrage free, is extremely rich and flexible, and has closed-form expressions for both European option values and local volatilities.The volatility surface is based on previous work by Carr and Pelts, for which the present authors provide a simple derivation and a concrete implementation.

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Author: Dr. Alexandre Antonov, Chief Analyst at Danske Bank

A 20 year Numerix veteran, Dr. Antonov is a Chief Analyst at Danske Bank in Copenhagen. Dr. Antonov received his PhD degree from the Landau Institute for Theoretical Physics in 1997 and joined Numerix in 1998, where he worked as a Senior Vice President of Quantitative Research. His activity is concentrated on modeling and numerical methods for interest rates, cross currency, hybrid, credit and CVA and FVA. Dr. Antonov is a published author for multiple publications in mathematical finance, including Risk magazine and a frequent speaker at financial conferences. He was named Risk Magazine's 2016 Quant of the Year. Most recently he served as a Director at Standard Chartered in London.

Author: Dr. Michael Konikov, Senior Vice President and Head of Quantitative Development, Numerix

Dr. Michael Konikov is a Senior Vice President and Head of Quantitative Development at Numerix, where he manages a team responsible for the development and delivery of models in Numerix software.  Previously, he worked at Citigroup, Barclays, and Bloomberg in quantitative research and desk quant roles.  He completed his PhD in mathematical finance at the University of Maryland College Park, concentrating, in particular, on the application of pure jump processes to option pricing.  Dr. Konikov's publications cover diverse asset classes ranging from equity to interest rates and credit. He has been published four technical articles in RISK Magazine on interest rate modeling, SABR model, and algorithmic differentiation for PV and XVA Greeks. Dr. Konikov is also co-author of the upcoming book Alexandre Antonov, Michael Konikov, Michael Spector “Modern SABR Analytics,” Springer (2019).

Author: Dr. Michael Spector, Vice President, Quantitative Research at Numerix

Dr. Michael Spector, VP of Quantitative Research, received his PhD in theoretical physics from the Budker Institute of Nuclear Physics, Novosibirsk. He has worked at research centers and universities in Russia, Israel, and the US and is the author of multiple publications on plasma physics, hydrodynamics, turbulence, nonlinear wave dynamics and mathematical finance. He joined the Numerix quantitative research team in 2006, working on the valuation of various exotic options (Asians, lookbacks, barriers), and has lately concentrated on the development of stochastic volatility models for interest rates and equity.

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New Arbitrage-Free Parametric Volatility Surface