Oxford University Postgraduate Case Studentship

MATHEMATICAL INSTITUTE AND ST CATHERINE’S COLLEGE, UNIVERSITY OF OXFORD, AND NOMURA

POSTGRADUATE CASE STUDENTSHIP

STUDENTSHIP: EPSRC STANDARD STUDENTSHIP + £2000 per annum enhancement + College and University fees.

Applications are invited for a postgraduate studentship, funded by EPSRC and Nomura, to work on the “Numerical Solution of a Class of SPDEs Arising in Finance” with Dr Christoph Reisinger (from the Mathematical and Computational Finance Group, part of the Mathematical Institute), and Reza Ghassemieh (Nomura). The studentship is for an October 2008 start, and is subject to standard Doctoral Training Account rules for eligibility.

It is generally acknowledged that present models in credit markets are insufficient for a reliable, quantitative assessment of the risk associated with structured products. Standard models impose a fairly simple dependence structure, which does not account for the impact the default of companies has on the credit quality of others. Due to computational limitations and restricted data availability, however, the treatment of large basket products so far proves elusive to a more flexible and realistic specification of the default contagion mechanism. We take an alternative route here, which models the evolution of the firm value distribution as a stochastic partial differential equation (SPDE).

The aims of the project are (a) to set up an SPDE model with macroscopic contagion effects; (b) to develop and analyse an accurate and robust numerical method for the PDE arising for a given realization of the stochastic market factors; (c) to derive estimators for default probabilities and credit spreads, and to minimize their variance by importance-sampling strategies; (d) to gain a better understanding of the absorbing boundary conditions; (e) to calculate parameter sensitivities and to calibrate the model to quoted market prices.