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Vibrato and Automatic Differentiation for High Order Derivatives and Sensitivities of Financial Options

Author

Listed:
  • Gilles Pagès

    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

  • Olivier Pironneau

    (LJLL - Laboratoire Jacques-Louis Lions - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

  • Guillaume Sall

    (LJLL - Laboratoire Jacques-Louis Lions - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique, LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper deals with the computation of second or higher order greeks of financial securities. It combines two methods, Vibrato and automatic differentiation and compares with other methods. We show that this combined technique is faster than standard finite difference, more stable than automatic differentiation of second order derivatives and more general than Malliavin Calculus. We present a generic framework to compute any greeks and present several applications on different types of financial contracts: European and American options, multidimensional Basket Call and stochastic volatility models such as Heston's model. We give also an algorithm to compute derivatives for the Longstaff-Schwartz Monte Carlo method for American options. We also extend automatic differentiation for second order derivatives of options with non-twice differentiable payoff.

Suggested Citation

  • Gilles Pagès & Olivier Pironneau & Guillaume Sall, 2017. "Vibrato and Automatic Differentiation for High Order Derivatives and Sensitivities of Financial Options," Post-Print hal-01234637, HAL.
    • Handle: RePEc:hal:journl:hal-01234637
    Note: View the original document on HAL open archive server: https://hal.science/hal-01234637v2
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    Cited by:

    1. S'ebastien Geeraert & Charles-Albert Lehalle & Barak Pearlmutter & Olivier Pironneau & Adil Reghai, 2017. "Mini-symposium on automatic differentiation and its applications in the financial industry," Papers 1703.02311, arXiv.org, revised Jun 2017.

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