Expected shortfall in credit portfolios with extremal dependence

We consider the risk of a portfolio comprised of loans, bonds, and financial instruments that are subject to possible default. We are interested in efficiently estimating expected excess loss conditioned on the event that the portfolio incurs large losses over a fixed time horizon; this risk measure is often referred to as expected shortfall. We consider a heterogeneous mix of obligors and assume a portfolio dependence structure that supports extremal dependence among obligors and does not hinge solely on correlation. We first derive sharp asymptotics that illustrate the implications of extremal dependence among obligors in the risk of the portfolio. Using this as a stepping stone, we develop a multistage importance sampling algorithm that is shown to have bounded relative error in estimating expected shortfall.