Ideas for MSc projects
Here are some outline ideas for computational projects for the
MSc in Mathematical and Computational Finance. MLMC refers to
Multilevel Monte Carlo, for which I have many references available from
https://people.maths.ox.ac.uk/gilesm/mlmc.html
and
https://people.maths.ox.ac.uk/gilesm/mlmc_community.html
These projects are all best suited to students with solid programming skills
in either python or C/C++. I can assist any students who are interested in
improving their C/C++ skills by using OpenMP for multi-threaded parallelisation.
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Use of adjoints for the efficient estimation of Greeks, in the context of
a) finite difference methods; b) Monte Carlo simulations
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Use of MLMC branching path simulations
(see arXiv paper)
to reduce variance of
a) bumping for Greeks, especially for digitals;
b) pathwise Greeks (combining ideas from this arXiv paper);
c) CDF estimation
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MLMC for quantile estimation following approach of Glynn and Blanchet
(see arXiv paper)
-
MLMC using approximate Lévy areas, as an alternative to the
technique described in this
arXiv paper
-
MLMC change of measure for complex digital options, as suggested in
my MCQMC12 review paper
on multilevel Monte Carlo methods, but not yet tried.
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MLMC for Lévy processes, based on
existing literature