We generalize the algorithmic differentiation method proposed by Antonov (2016) from price Greeks to XVA Greeks. This method, named Backward Differentiation (BD), was developed in the context of computing price or PV Greeks for individual callable exotic trades.

We start by treating cases where cashflow derivatives are sufficient for computing PV/XVA Greeks, i.e., where the differentiation of conditional expectations (or regression functions) is not necessary. For example, PV Greeks for Bermudan swaptions can be computed without having to perform the complicated step of regression function differentiation. We modify the Backward Differentiation algorithm to calculate Greeks for such instruments: the method is applied during the backward pricing procedure and has almost no overhead with respect to a pure backward pricing (without the Greeks).

A general XVA calculation cannot be done using only the cashflow derivatives - some exceptions are listed in this article - instead, the differentiation of future instrument values that are results of the regression may be required. We leverage the algorithmic calculation of future values (Algorithmic Exposures) and describe the Adjoint Differentiation (AD) and the new BD for XVA Greeks. The latter algorithm is much simpler than the former, in particular, it does require the use of the instrument tape, i.e., it does not require the storage of certain payoff derivatives during the pricing procedure as is the case for AD. At the same time, both AD and BD enjoy a similar level of performance.

Complete the form to download this research paper, “PV and XVA Greeks for Callable Exotics by Algorithmic Differentiation”

About the Authors:

Dr. Alexandre Antonov, Senior Vice President of Quantitative Research, Numerix
Dr. Antonov was recently recognized with 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.

Dr. Michael Konikov, Senior Vice President and Head of Quantitative Development, Numerix
Dr. Konikov is a Senior Vice President and the Head of Quantitative Development at Numerix, where he manages a team of quant developers and is responsible for the development and delivery of models in Numerix software. Prior to Numerix, he worked at Citigroup, Barclays, and Bloomberg in quantitative research and desk quant roles. He completed his PhD in mathematics at the University of Maryland College Park, concentrating on mathematical finance and, in particular, the application of pure jump processes to option pricing. Dr. Konikov has publications in mathematical finance covering diverse asset classes ranging from equity to interest rates and credit.

Dr. Serguei Issakov, Global Head of Quantitative Research, Numerix
Dr. Issakov, as Global Head of Quantitative Research, oversees the company’s quantitative research globally, including the research of pricing models at Numerix. Since joining Numerix in 1999, his earlier roles at Numerix included Vice President of Financial Applications, Head of Engine Development (the forerunner to Numerix 7) and Head of Risk Analytics.Prior to joining Numerix, Dr. Issakov held research positions in theoretical physics at the Nordic Institute for Theoretical Physics in Copenhagen, the University of Paris (Laboratory of Theoretical Physics and Statistical Models), the University of Oslo and the Center for Advanced Study in Oslo. Before that, he led research on models of brain rhythms at the Medical Radiological Center in Obninsk Russia. Dr. Issakov has published over 40 papers in mathematics and theoretical physics. He is a co-author of the Issakov-Ouvry-Wu equations in fundamental quantum statistical mechanics. He has received numerous fellowships and research grants, including a NATO Visiting Professorship and grants from the Russian Foundation for Basic Research. He holds PhD in Theoretical and Mathematical Physics from Moscow Institute of Physics and Technology, from the Theory Group led by Physics Nobel Laureate Vitaly Ginzburg.

Dr. Andrew McClelland, PhD, Director of Quantitative Research, Numerix
Andrew McClelland’s quantitative research at Numerix focuses on XVA pricing and hedging, generating counterparty credit risk metrics for structured products, and estimating risk model parameters via time-series estimation. He earned his PhD in finance at the Queensland University of Technology for a thesis on financial econometrics. He considered markets exhibiting crash feedback, option pricing for such markets, and parameter estimation for such markets using particle filtering methods. Dr. McClelland’s work has been published in the Journal of Banking and Finance, the Journal of Econometrics, and the Journal of Business and Economic Statistics.

Dr.Serguei Mechkov, Senior Vice President of Quantitative Research, Numerix

Download Numerix Research Paper

Complete the form below to download this complimentary research paper.

Select Form: 

Form #5: Research

Keep me informed of future research from Numerix:

Sign me up to receive "Thinking Derivatively" monthly newsletter by Numerix:

* Required fields
written blog

The Market Impact of SOFR Discounting: What We Know So Far

press release - Feb 12, 2020

CubeLogic and Numerix partnership yields rapid results - Two new client signings within eight months

white paper

White paper | The Capital Markets 2020: In the Eye of Two Storms

on-demand webinar

The LIBOR Transition in 2020: Roundtable Discussion with Numerix and Greenwich Associates

newsletter issue - Jan 29, 2020

Thinking Derivatively – January/February 2020 Newsletter

white paper

White paper | Analyzing the Market Impact of SOFR Discounting

analyst report

Greenwich Associates EBook: Trading, Technology and the LIBOR Transition

conference

GARP Risk Convention 2020

journal issue

Numerix Journal Vol. 6, No. 1

in the news - Dec 16, 2019

Numerix to eye more acquisitions in 2020, CEO says

newsletter issue - Dec 11, 2019

Thinking Derivatively - December 2019 Issue

on-demand webinar

Applying AI to Streamline the LIBOR Transition