14:15
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.