Calculating the Greeks by cubature formulae
Copyright policy )Calculating the Greeks by cubature formulae
We provide cubature formulae for the calculation of derivatives of expected values in the spirit 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 formulae for Greeks is based on universal formulae, which lead to the calculation of Greeks in an asymptotic sense—even without Hörmander's condition. Cubature formulae then allow to calculate these quantities very quickly. Simple examples are added to the theoretical exposition.
- TU Wien Austria
nilpotent Lie groups, Stochastic calculus of variations and the Malliavin calculus, Probability (math.PR), Applications of stochastic analysis (to PDEs, etc.), Numerical Analysis (math.NA), Finance etc., Numerical quadrature and cubature formulas, Stochastic ordinary differential equations (aspects of stochastic analysis), Hörmander's theorem, Wiener space, FOS: Mathematics, Malliavin Calculus, Mathematics - Numerical Analysis, 60H07, 35R60, 65C30, cubature formulae, Mathematics - Probability
nilpotent Lie groups, Stochastic calculus of variations and the Malliavin calculus, Probability (math.PR), Applications of stochastic analysis (to PDEs, etc.), Numerical Analysis (math.NA), Finance etc., Numerical quadrature and cubature formulas, Stochastic ordinary differential equations (aspects of stochastic analysis), Hörmander's theorem, Wiener space, FOS: Mathematics, Malliavin Calculus, Mathematics - Numerical Analysis, 60H07, 35R60, 65C30, cubature formulae, Mathematics - Probability
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