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Real-time risk management: An AAD-PDE approach

Author

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  • Luca Capriotti

    (Quantitative Strategies, Investment Banking Division, Credit Suisse Group, One Cabot Square, London E14 4QJ, UK†Department of Mathematics, University College London, London WC1E 6BT, UK)

  • Yupeng Jiang

    (#x2020;Department of Mathematics, University College London, London WC1E 6BT, UK)

  • Andrea Macrina

    (#x2020;Department of Mathematics, University College London, London WC1E 6BT, UK‡Department of Actuarial Science, University of Cape Town, Rondebosch 7701, South Africa)

Abstract

We apply adjoint algorithmic differentiation (AAD) to the risk management of securities when their price dynamics are given by partial differential equations (PDE). We show how AAD can be applied to forward and backward PDEs in a straightforward manner. In the context of one-factor models for interest rates or default intensities, we show how price sensitivities are computed reliably and orders of magnitude faster than with a standard finite-difference (FD) approach. This significantly increased efficiency is obtained by combining (i) the adjoint forward PDE for calibrating model parameters, (ii) the adjoint backward PDE for derivatives pricing, and (iii) the implicit function theorem to avoid iterating the calibration procedure.

Suggested Citation

  • Luca Capriotti & Yupeng Jiang & Andrea Macrina, 2015. "Real-time risk management: An AAD-PDE approach," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 1-31, December.
    • Handle: RePEc:wsi:ijfexx:v:02:y:2015:i:04:n:s2424786315500395
    DOI: 10.1142/S2424786315500395
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    References listed on IDEAS

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    1. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
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    Cited by:

    1. Cornelis S. L. de Graaf & Drona Kandhai & Christoph Reisinger, 2016. "Efficient exposure computation by risk factor decomposition," Papers 1608.01197, arXiv.org, revised Feb 2018.

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