Mike Giles - Multilevel Monte Carlo software

Multilevel Quasi-Monte Carlo software

On this page I provide software for MLQMC computations using MATLAB. In the future, we will also develop a C/C++ version and possibly a Python version.

Each application code has two parts, a high-level part which calls "mlqmc_test" to perform the MLQMC tests, using the routine "mlqmc", and a low-level part which is called by both "mlqmc_test" and "mlqmc" to compute the MLQMC differences for one particular level of correction.

The application codes produce one or more output text files. The MATLAB routine "mlmc_plot" can then be used to generate the standard set of figures which I use in most of my papers.

MATLAB

Common routines used by all applications:

mlqmc.m -- main MLQMC driver routine
mlqmc_test.m -- routine for MLQMC tests
mlqmc_plot.m -- routine for plotting results
mlqmc_pt_gen.m -- routine to generate QMC points
bb.m -- Brownian Bridge routine
rank_1.m -- rank 1 lattice generator
z_d4096_m15_gf1.mat -- data file used by rank_1.m
ncf.m and ncfinv.m -- Normal CDF and its inverse

mcqmc06 -- financial options based on scalar geometric Brownian motion, similar to my MCQMC06 paper, using a Milstein discretisation

mcqmc06.m -- application code
mcqmc06.tex -- LaTeX file for output
mcqmc06.pdf -- PDF results

basket -- basket options based on 5 underlying assets, similar to my 2009 Winter Simulation Conference paper, using a Milstein discretisation

basket.m -- application code
basket.tex -- LaTeX file for output
basket.pdf -- PDF results

C/C++

Common routines used by all applications:

mcqmc06 -- financial options based on scalar geometric Brownian motion, similar to MCQMC06 paper, using a Milstein discretisation

Licensing and acknowledgements

This software is freely available to all under a GPL license -- anyone requiring a more permissive license for commercial purposes should contact me.

The software is based on the research reported in the papers listed here. In particular, for the MLQMC work see

M.B. Giles and B.J. Waterhouse. 'Multilevel quasi-Monte Carlo path simulation'. pp.165-181 in Advanced Financial Modelling, in Radon Series on Computational and Applied Mathematics, de Gruyter, 2009. (PDF)

If you find it helpful in your research, this paper can be cited in any publications. I would also be interested to hear about it, particularly if it is used for novel applications.

The underlying research has been supported by

EPSRC, through a Springboard Fellowship and project funding
Oxford-Man Institute of Quantitative Finance