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

Gilles Pagès (1) , Olivier Pironneau (2) , Guillaume Sall (2, 1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 LJLL - Laboratoire Jacques-Louis Lions

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.

Mots clés: Vibrato; Automatic Differentiation; High Order Derivative; Greeks; Monte Carlo Method; Option Pricing; Path-Dependent Option; High Dimension; Euler Scheme

Domaines: Analyse numérique [cs.NA]; Finance quantitative [q-fin.CP]

Gilles Pagès, Olivier Pironneau, Guillaume Sall. Vibrato and Automatic Differentiation for High Order Derivatives and Sensitivities of Financial Options. 2015. ⟨hal-01234637v1⟩