Higher Order weak approximation of Stochastic Differential Equations with application to finance

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The following 5 results are achieved: [1] A new higher order algorithm for pricing barrier-type derivatives is found. [2] A computer program library of Kusuoka approximation for general SDEs are constructed and made public. [3] A new family of stochastic variables that enables 7th order weak approximation is constructed. [4] A new variable transformation method for Heston stochastic volatility models found. The transformed Heston model can be calculated faster by the NN algorithm. [5] A new index process from which we can detect lead/lag relations between two stochastic processes is constructed.Results [1][2] and [3] are expected from the beginning of this research project. [4] and [5] are the spin-offs of the main project.