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Fast Correlation Greeks by Adjoint Algorithmic Differentiation

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  • Luca Capriotti
  • Mike Giles

Abstract

We show how Adjoint Algorithmic Differentiation (AAD) allows an extremely efficient calculation of correlation Risk of option prices computed with Monte Carlo simulations. A key point in the construction is the use of binning to simultaneously achieve computational efficiency and accurate confidence intervals. We illustrate the method for a copula-based Monte Carlo computation of claims written on a basket of underlying assets, and we test it numerically for Portfolio Default Options. For any number of underlying assets or names in a portfolio, the sensitivities of the option price with respect to all the pairwise correlations is obtained at a computational cost which is at most 4 times the cost of calculating the option value itself. For typical applications, this results in computational savings of several order of magnitudes with respect to standard methods.

Suggested Citation

  • Luca Capriotti & Mike Giles, 2010. "Fast Correlation Greeks by Adjoint Algorithmic Differentiation," Papers 1004.1855, arXiv.org.
    • Handle: RePEc:arx:papers:1004.1855
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    Cited by:

    1. Siamak Akbarzadeh & Jan Hückelheim & Jens-Dominik Müller, 2020. "Consistent treatment of incompletely converged iterative linear solvers in reverse-mode algorithmic differentiation," Computational Optimization and Applications, Springer, vol. 77(2), pages 597-616, November.
    2. Shuaiqiang Liu & Lech A. Grzelak & Cornelis W. Oosterlee, 2022. "The Seven-League Scheme: Deep Learning for Large Time Step Monte Carlo Simulations of Stochastic Differential Equations," Risks, MDPI, vol. 10(3), pages 1-27, February.
    3. Cristian Homescu, 2011. "Adjoints and Automatic (Algorithmic) Differentiation in Computational Finance," Papers 1107.1831, arXiv.org.
    4. Jain, Shashi & Oosterlee, Cornelis W., 2015. "The Stochastic Grid Bundling Method: Efficient pricing of Bermudan options and their Greeks," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 412-431.

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