Numerical Valuation of Basket Credit Derivatives in Structural Jump-Diffusion Models

We consider a model where each company's asset value follows a jump-di usion
process, and is connected with other companies via global factors. Motivated by
ideas in Bush et al. (2011), where the joint density of asset values is evolved in a
large basket approximation, we develop an algorithm for the e cient estimation of
CDO index and tranche spreads consistent with underlying CDSs, through a nite
di erence simulation of the resulting SPDE. We verify the validity of this approximation
numerically by comparison to results obtained by direct Monte Carlo simulation
of the basket constituents. A calibration exercise assesses the
exibility of the model
and its extensions to match CDO spreads from pre-crisis and crisis periods.