Two-Level Simulations for Risk Measurement
Jeremy Staum
Department of Industrial Engineering and Management Sciences
Northwestern University
Wednesday, February 13, 2008
4:30 - 5:30 PM
Terman Engineering Center, Room 453
Abstract:
Risk measurement involves estimating some functional of the distribution of loss. Monte Carlo simulation is often used to estimate the mean of a distribution, but some risk measures, such as value at risk and tail conditional expectation, are not means of a distribution from which one can sample. This calls for nested simulation, in which risk factors are sampled at an outer level of simulation, while the inner level of simulation provides estimates of loss given each realization of the risk factors. In our examples, the outer level simulates tomorrow's stock prices, and the inner level estimates the loss of a portfolio of stock options given tomorrow's stock prices. We present a general method for providing a confidence interval for the risk measurement given statistical error at two levels of simulation. This method could require a large computational budget, so we discuss efficient procedures for providing a confidence interval and point estimates for tail conditional expectation.
Operations Research Colloquia: http://or.stanford.edu/oras_seminars.html