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Adjoints and Automatic (Algorithmic) Differentiation in Computational Finance

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  • Cristian Homescu

Abstract

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.

Suggested Citation

  • Cristian Homescu, 2011. "Adjoints and Automatic (Algorithmic) Differentiation in Computational Finance," Papers 1107.1831, arXiv.org.
    • Handle: RePEc:arx:papers:1107.1831
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Gabriel Turinici, 2009. "Calibration of local volatility using the local and implied instantaneous variance," Post-Print hal-00338114, HAL.
    4. 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.
    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. Joshi, Mark & Pitt, David, 2010. "Fast Sensitivity Computations for Monte Carlo Valuation of Pension Funds," ASTIN Bulletin, Cambridge University Press, vol. 40(2), pages 655-667, November.
    7. Joshi, Mark & Yang, Chao, 2011. "Efficient greek estimation in generic swap-rate market models," Algorithmic Finance, IOS Press, vol. 1(1), pages 17-33.
    8. Luca Capriotti & Mike Giles, 2010. "Fast Correlation Greeks by Adjoint Algorithmic Differentiation," Papers 1004.1855, arXiv.org.
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    Cited by:

    1. L. Jeff Hong & Sandeep Juneja & Jun Luo, 2014. "Estimating Sensitivities of Portfolio Credit Risk Using Monte Carlo," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 848-865, November.
    2. Cristian Homescu, 2011. "Implied Volatility Surface: Construction Methodologies and Characteristics," Papers 1107.1834, arXiv.org.
    3. Joshi, Mark & Tang, Robert, 2014. "Effective sub-simulation-free upper bounds for the Monte Carlo pricing of callable derivatives and various improvements to existing methodologies," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 25-45.

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