Price sensitivities to risk factors, otherwise known as Greeks, have recently been just as challenging to calculate as they are essential in efficient risk management and regulatory reporting. This is especially true in the case of derivatives with early exercise features, such as Bermudan options, where exercise is allowed at certain specified dates before expiration.

It becomes even more complicated and time-consuming when one has to price valuation adjustments (XVAs) for these instruments, as this involves computation of the future values of the derivative at each exercise point.

Distributions of future values are computed using Monte Carlo simulations and regression. Finding Greeks, on the other hand, requires differentiation of these regressions at each future value, which can be computationally very intensive.

In this Cutting Edge research article published in the January 2018 Issue of Risk Magazine, Drs. Alexander Antonov, Serguei Issakov, Michael Konikov, Andy McClelland, and Serguei Mechkov maintain that differentiation of regressions can be avoided for some derivatives instruments and highlights how avoiding differentiation has two advantages – speed and accuracy. Using a new Numerix technique, Greeks can be computed almost as quickly as the time it takes to price the derivatives. Cutting the step of differentiating regressions also helps reduce noise in the estimation.

Authors: Drs. Alexander Antonov, Serguei Issakov, Michael Konikov, Andy McClelland, Serguei Mechkov

Dr. Alexandre Antonov, Member of Quantitative Advisory Board, Numerix

Dr. Antonov received his PhD degree from the Landau Institute for Theoretical Physics in 1997 and held a quantitative research role at Numerix from 1998 until 2017. Today, he sits on Numerix’s Quantitative Advisory Board. At Numerix, his activity was 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 is a frequent speaker at financial conferences.

 

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