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

Gilles Pagès (), Olivier Pironneau and Guillaume Sall ()
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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

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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.

Keywords: Vibrato; Automatic Differentiation; High Order Derivative; Greeks; Monte Carlo Method; Option Pricing; Path-Dependent Option; High Dimension; Euler Scheme (search for similar items in EconPapers)
Date: 2017
Note: View the original document on HAL open archive server: https://hal.science/hal-01234637v2
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Published in The Journal of Computational Finance, 2017

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01234637

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