ANALYTIC APPROXIMATION TO LOSS DISTRIBUTIONS OF HETEROGENEOUS PORTFOLIOS

摘要

In this paper we discuss the analytic approximation to the loss distribution of large conditionally independent heterogeneous portfolios. We first apply the Esseen's inequality to show that the overall loss distribution can be approximated accurately and computed efficiently by the integration of a normal distribution function. We then discuss the portfolio risk measures (VaR and CVaR) and show that they can be easily derived by solving a linear programming problem where VaR is the optimal solution and CVaR is the optimal value. Finally we illustrate with two examples that the analytic approximation is less suitable in studying the extreme value of tail distributions.