  The computation of Greeks is a fundamental task for risk managing of
financial instruments. The standard approach to their numerical evaluation is
via finite differences. Most exotic derivatives are priced via Monte Carlo
simulation: in these cases, it is hard to find a fast and accurate
approximation of Greeks, mainly because of the need of a tradeoff between bias
and variance. Recent improvements in Greeks computation, such as Adjoint
Algorithmic Differentiation, are unfortunately uneffective on second order
Greeks (such as Gamma), which are plagued by the most significant
instabilities, so that a viable alternative to standard finite differences is
still lacking. We apply Chebyshev interpolation techniques to the computation
of spot Greeks, showing how to improve the stability of finite difference
Greeks of arbitrary order, in a simple and general way. The increased
performance of the proposed technique is analyzed for a number of real payoffs
commonly traded by financial institutions.
