Real-Time Risk Management: An AAD-PDE Approach

32 Pages Posted: 15 Jul 2015

See all articles by Luca Capriotti

Luca Capriotti

University College London; NYU Polytechnic School of Engineering - Department of Finance and Risk Engineering

Yupeng Jiang

University College London

Andrea Macrina

University College London; University of Cape Town (UCT)

Date Written: June 22, 2015

Abstract

We apply adjoint algorithmic differentiation (AAD) to the risk management of derivative securities in the situation where the dynamics of securities prices are given in terms of partial differential equations (PDE). With simple examples, we show how AAD can be applied to both forward and backward PDEs in a straightforward manner. In particular, in the context of one-factor short-rate models for interest rates or default intensity processes, we show how one can compute price sensitivities reliably and orders of magnitude faster than with a standard finite-difference approach. This significantly increased efficiency is obtained by combining (i) the adjoint of a forward PDE for calibrating the parameters of the model, (ii) the adjoint of a backward PDE for pricing the derivative security, and (iii) the implicit function theorem to avoid iterating the calibration procedure.

Keywords: Adjoint Algorithmic Differentiation, Partial Differential Equations, Credit Derivatives

Suggested Citation

Capriotti, Luca and Jiang, Yupeng and Macrina, Andrea, Real-Time Risk Management: An AAD-PDE Approach (June 22, 2015). Available at SSRN: https://ssrn.com/abstract=2630328 or http://dx.doi.org/10.2139/ssrn.2630328

Luca Capriotti (Contact Author)

University College London ( email )

Gower Street
London, WC1E 6BT
United Kingdom

NYU Polytechnic School of Engineering - Department of Finance and Risk Engineering ( email )

Brooklyn, NY 11201
United States

Yupeng Jiang

University College London ( email )

Gower Street
London, WC1E 6BT
United Kingdom

Andrea Macrina

University College London ( email )

Gower Street
London, WC1E 6BT
United Kingdom

University of Cape Town (UCT) ( email )

Private Bag X3
Rondebosch, Western Cape 7701
South Africa

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