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Algorithmic Differentiation For Discontinuous Payoffs

Author

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  • ROBERTO DALUISO

    (Interest Rate and Credit Models, Banca IMI, Largo Mattioli 6, 20100 Milan, Italy†Department of Statistics and Quantitative Methods, Milano-Bicocca University, U7 Building, Via Bicocca degli Arcimboldi 8, 20126 Milan, Italy)

  • GIORGIO FACCHINETTI

    (Interest Rate and Credit Models, Banca IMI, Largo Mattioli 6, 20100 Milan, Italy)

Abstract

We present a general technique to compute the sensitivities of the Monte Carlo prices of discontinuous financial products. It is a natural extension of the pathwise adjoints method, which would require an almost-surely differentiable payoff; the efficiency of the latter method when many sensitivities must be calculated is preserved. We show empirically that the new algorithm is competitive in terms of accuracy and execution time when compared to benchmarks obtained by smoothing of the payoff, which benchmarks are biased and require a nonobvious tuning of their parameters.

Suggested Citation

  • Roberto Daluiso & Giorgio Facchinetti, 2018. "Algorithmic Differentiation For Discontinuous Payoffs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-41, June.
    • Handle: RePEc:wsi:ijtafx:v:21:y:2018:i:04:n:s021902491850019x
    DOI: 10.1142/S021902491850019X
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    References listed on IDEAS

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    1. Capriotti, Luca, 2015. "Likelihood Ratio Method and Algorithmic Differentiation: Fast Second Order Greeks," Algorithmic Finance, IOS Press, vol. 4(1-2), pages 81-87.
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    Cited by:

    1. Roberto Daluiso, 2023. "Fast and Stable Credit Gamma of CVA," Papers 2311.11672, arXiv.org.

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