Analytic Approximation to Loss Distributions of Heterogeneous Portfolios

In this talk we discuss the analytic approximation to the loss

distribution of large conditionally independent heterogeneous portfolios. The

loss distribution is approximated by the expectation of some normal

distributions, which provides good overall approximation as well as tail

approximation. The computation is simple and fast as only numerical

integration is needed. The analytic approximation provides an excellent

alternative to some well-known approximation methods. We illustrate these

points with examples, including a bond portfolio with correlated default risk

and interest rate risk. We give an analytic expression for the expected

shortfall and show that VaR and CVaR can be easily computed by solving a

linear programming problem where VaR is the optimal solution and CVaR is the

optimal value.