Efficient Nested Simulation Of Tail Risk Measures

Tail risk estimation for portfolios of complex financial instruments is an important enterprise risk management task. Time consuming nested simulations are usually required for such tasks: The outer loop simulates the evolution of risk factors, or the scenarios. Inner simulations are then conducted in each scenario to estimate the corresponding portfolio losses, whose distribution entails the tail risk of interest. In this paper we propose an iterative procedure, called Importance-Allocated Nested Simulation (IANS), for tail risk estimation. We tested IANS in a multiple-period nested simulation setting for an actuarial application. Our numerical results show that IANS can be an order of magnitude more accurate that a standard nested simulation procedure.