Discrete Algorithms for Multivariate Financial Calculus

Quantitative financial calculus is dominated by calculations of integrals related to various moments of probability distributions used for modelling. Here, we develop a general technique that facilitates the numerical calculations of options, prices for the difficult case of mult-assets, for the majority of European payoff contracts. The algorithms proposed here rely on known weak convergence results, hence making use of the gaussian probability kernel even when modelling with non-gaussian distributions. In addition, this technique can be employed for calculating greek parameter. We prove that the weak convergence characterizing condition can still be applied under some mild assumption on the payoff function of financial options.