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.

- Use of adjoints for the efficient estimation of Greeks, in the context of a) finite difference methods; b) Monte Carlo simulations
- 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
- 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.
- MLMC for Lévy processes, based on existing literature