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

摘要

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.