Calculating the Greeks by Cubature Formulas

We provide cubature formulas for the calculation of derivatives of expected values in the spririt of Terry Lyons and Nicolas Victoir. In financial mathematics derivatives of option prices with respect to initial values, so called Greeks, are of particular importance as hedging parameters. The proof of existence of Cubature formulas for Greeks is based on an argument, which leads to the calculation of Greeks in an asymptotic sense – even without Hörmander’s condition. Cubature formulas then allow to calculate these quantities very quickly. Simple examples are added to the theoretical exposition.