Construction of moment-matching multinomial lattices using Vandermonde matrices and Gröbner bases

Citation:
Lundengård K, Ogutu C, Silvestrov S, Weke P. Construction of moment-matching multinomial lattices using Vandermonde matrices and Gröbner bases.; 2017.

Abstract:

In order to describe and analyze the quantitative behavior of stochastic processes, such as
the process followed by a financial asset, various discretization methods are used. One such
set of methods are lattice models where a time interval is divided into equal time steps and
the rate of change for the process is restricted to a particular set of values in each time step.
The well-known binomial-and trinomial models are the most commonly used in applications,
although several kinds of higher order models have also been examined. Here we will
examine various ways of designing higher order lattice schemes with different node
placements in order to guarantee moment-matching with the process.

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