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AAD and Least Squares Monte Carlo: Fast Bermudan-style Options and XVA Greeks

Written by Luca Capriotti, Yupeng Jiang and Andrea Macrina.  Luca Capriotti, Head of Quantitative Strategies Credit Products and Structures Notes at Credit Suisse will be presenting at Global Derivatives 2017: "AAD & Least Square Monte Carlo: Fast XVA & Bermudan Greeks".

ABSTRACT: We show how Adjoint Algorithmic Differentiation (AAD) can be used to calculate price sensitivities in regression based Monte Carlo methods reliably and orders of magnitude faster than with standard finite-differences approaches. By discussing in detail examples of practical relevance, we demonstrate how accounting for the contributions associated with the regression functions is crucial to obtain accurate estimates of the Greeks for Bermudan-style options and XVA applications.

The efficient calculation of the risk factor sensitivities of financial derivatives, also known as the “Greeks”, is an essential component of modern risk management practices. Indeed, the aftermath of the recent financial crisis has seen remarkable changes in the market practice whereby financial institutions need to quantify (and risk-manage) counterparty, funding and capital risk exposures, collectively known as XVA, in large portfolios, see e.g. Crépey et al. (2014).

The traditional approach for the calculation of the Greeks is the so-called bump and reval or bumping technique. This comes with a significant computational cost as it generally requires repeating the calculation of the P&L of a portfolio under hundreds of market scenarios in order to form finite-difference estimators.
As a result, in many cases, even after deploying vast amounts of computer power, these calculations cannot be completed in a practical amount of time. Conversely, Adjoint Algorithmic Differentiation (AAD), a numerical technique recently introduced to
financial engineering (see e.g., Capriotti (2011), Capriotti et al. (2011), Capriotti and Giles (2010, 2012), Henrard (2011)), has proven to be effective for speeding up the calculation of risk factor sensitivities, both for Monte Carlo (MC) and deterministic numerical methods, see Capriotti and Lee (2014) and Capriotti
et al. (2015).

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