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

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.
Type de document :
Pré-publication, Document de travail
2015
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https://hal.archives-ouvertes.fr/hal-01234637
Contributeur : Olivier Pironneau <>
Soumis le : vendredi 22 janvier 2016 - 14:30:38
Dernière modification le : jeudi 27 avril 2017 - 09:46:20

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Draft-Vibratov5.pdf
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  • HAL Id : hal-01234637, version 2

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UPMC | LJLL | USPC | PMA

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Gilles Pages, Olivier Pironneau, Guillaume Sall. Vibrato and Automatic Differentiation for High Order Derivatives and Sensitivities of Financial Options. 2015. <hal-01234637v2>

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