Journal of Computational Finance

Risk.net

Vibrato and automatic differentiation for high-order derivatives and sensitivities of financial options

Gilles Pagès, Olivier Pironneau and Guillaume Sall

  • The computation of second or higher order greeks of financial securities is analyzed. 
  • A combining Vibrato and automatic differentiation is proposed.
  • It is shown why computation by finite difference for trends should be discarded.
  • The method applies tor European and American options, multidimensional Basket Call and stochastic volatility models.
  • An implementation of automatic differentiation for second order derivatives bypassing non differentiability is proposed.

This paper deals with the computation of second-order or higher Greeks of financial securities. It combines two methods, vibrato and automatic differentiation (AD), and compares these with other methods. We show that this combined technique is faster and more stable than AD of second-order derivatives or finite-difference approximations. We present a generic framework to compute any Greeks and discuss several applications to different types of European and American contracts. We also extend AD for second-order derivatives of options with non-twice-differentiable payoff.

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