Discipline: 
Mathematics
Status: 
Available
Level: 
Summer Project
Supervisor(s): 
Dr Duy-Minh Dang

Suitable for:  Master/Honours students with an excellent background in computational mathematics and a strong interest/background in finance (eg Master of Financial Mathematics).

Project:  The project is motivated by a number of significant new computational challenges arising from the computation of valuation adjustments, collectively referred to as xVA, of over-the-counter derivatives and risk-management (hedging) of associated risks, as required by the on-going financial regulatory reform in response to the 2007-2008.  We focus on adapting the novel hybrid Monte Carlo and Partial Differential Equation approach developed in Dang et al (2015) for computation of xVA of exotic options under the Heston and Heston-Hull-White models.  The core of the method is the derivation of an approximation to the solution of the conditional PIDE using a Fourier cosine or Shannon wavelet expansions.

Expected outcomes:  A successful project should lead to a publishable paper.

Duration:  10 weeks; start date is flexible, but preferably by the last week of November.

Contact:  Dr Duy-Minh Dang, duyminh.dang@uq.edu.au or phone +61 7 336 52686 or 0432 945883

References: 

Duy-Minh Dang, Ken Jackson and Mohammadreza Mohammadi, Applied Mathematical Finance 22 (5) (2015), pp. 522-552.

Duy-Minh Dang, A multi-level dimension reduction Monte-Carlo method for jump-diffusion models, Journal of Computational and Applied Mathematics 324 (2017), pp. 49-71.

Duy-Minh Dang and Luis Ortiz-Gracia, A dimension reduction Shannon-wavelet based method for option pricing, Journal of Scientific Computing (to appear).

Duy-Minh Dang, Ken Jackson, and Scott Sues, A dimension and variance reduction Monte Carlo method for pricing and hedging options under jump-diffusion models, Applied Mathematical Finance (to appear).

Edouard Berth, Duy-Minh Dang, and Luis Ortiz-Gracia, A Shannon wavelet method for foreign exchange options under the Heston multi-factor CIR model (submitted).