## 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:

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

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

### 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