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Adjoints and Automatic (Algorithmic) Differentiation in Computational Finance

  • Cristian Homescu
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    Two of the most important areas in computational finance: Greeks and, respectively, calibration, are based on efficient and accurate computation of a large number of sensitivities. This paper gives an overview of adjoint and automatic differentiation (AD), also known as algorithmic differentiation, techniques to calculate these sensitivities. When compared to finite difference approximation, this approach can potentially reduce the computational cost by several orders of magnitude, with sensitivities accurate up to machine precision. Examples and a literature survey are also provided.

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    File URL: http://arxiv.org/pdf/1107.1831
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    Paper provided by arXiv.org in its series Papers with number 1107.1831.

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    Date of creation: Jul 2011
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    Handle: RePEc:arx:papers:1107.1831
    Contact details of provider: Web page: http://arxiv.org/

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    1. Mark Joshi & Chao Yang, 2010. "Fast And Accurate Pricing And Hedging Of Long-Dated Cms Spread Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(06), pages 839-865.
    2. Mark Joshi & Alexander Wiguna, 2012. "Accelerating Pathwise Greeks In The Libor Market Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1250012-1-1.
    3. C. Kaebe & J. Maruhn & E. Sachs, 2009. "Adjoint-based Monte Carlo calibration of financial market models," Finance and Stochastics, Springer, vol. 13(3), pages 351-379, September.
    4. Joshi, Mark & Yang, Chao, 2011. "Efficient greek estimation in generic swap-rate market models," Algorithmic Finance, IOS Press, vol. 1(1), pages 17-33.
    5. Houtan Bastani & Luca Guerrieri, 2008. "On the application of automatic differentiation to the likelihood function for dynamic general equilibrium models," International Finance Discussion Papers 920, Board of Governors of the Federal Reserve System (U.S.).
    6. Luca Capriotti & Mike Giles, 2010. "Fast Correlation Greeks by Adjoint Algorithmic Differentiation," Papers 1004.1855, arXiv.org.
    7. Gabriel Turinici, 2009. "Calibration of local volatility using the local and implied instantaneous variance," Post-Print hal-00338114, HAL.
    8. Joshi, Mark & Yang, Chao, 2011. "Fast delta computations in the swap-rate market model," Journal of Economic Dynamics and Control, Elsevier, vol. 35(5), pages 764-775, May.
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