Numerical valuation of basket credit derivatives in structural jump-diffusion models

We consider a model where each company's asset value follows a jump-diffusion process and is connected with other companies via global factors. Motivated by the 2011 work of Bush, Hambly, Haworth, Jin and Reisinger, where the joint density of asset values is evolved in a large basket approximation, we develop an algorithm for the efficient estimation of collateralized debt obligation (CDO) index and tranche spreads consistent with underlying credit default swaps, using a finite difference simulation of the resulting stochastic partial differential equation. We verify the validity of this approximation numerically by comparison with results obtained by direct Monte Carlo simulation of the basket constituents. A calibration exercise assesses the flexibility of the model and its extensions to match CDO spreads from precrisis and crisis periods.