Parallelization of the α‐stable modelling algorithms

Abstract

Stable distributions have a wide sphere of application: probability theory, physics, electronics, economics, sociology. Particularly important role they play in financial mathematics, since the classical models of financial market, which are based on the hypothesis of the normality, often become inadequate. However, the practical implementation of stable models is a nontrivial task, because the probability density functions of α‐stable distributions have no analytical representations (with a few exceptions). In this work we exploit the parallel computing technologies for acceleration of numerical solution of stable modelling problems. Specifically, we are solving the stable law parameters estimation problem by the maximum likelihood method. If we need to deal with a big number of long financial series, only the means of parallel technologies can allow us to get results in a adequate time. We have distinguished and defined several hierarchical levels of parallelism. We show that coarse‐grained Multi‐Sets parallelization is very efficient on computer clusters. Fine‐grained Maximum Likelihood level is very efficient on shared memory machines with Symmetric multiprocessing and Hyper‐threading technologies. Hybrid application, which is utilizing both of those levels, has shown superior performance compared to single level (MS) parallel application on cluster of Pentium 4 HT nodes.

Key words:

• Parallel algorithms
• stable modelling
• financial mathematics