Nested Simulation in Portfolio Risk Measurement
by Michael B. Gordy of the Federal Reserve Board, and
April 8, 2008
Abstract: Risk measurement for derivative portfolios almost invariably calls for nested simulation. In the outer step one draws realizations of all risk factors up to the horizon, and in the inner step one re-prices each instrument in the portfolio at the horizon conditional on the drawn risk factors. Practitioners may perceive the computational burden of such nested schemes to be unacceptable, and adopt a variety of second-best pricing techniques to avoid the inner simulation. In this paper, we question whether such short cuts are necessary. We show that a relatively small number of trials in the inner step can yield accurate estimates, and analyze how a fixed computational budget may be allocated to the inner and the outer step to minimize the mean square error of the resultant estimator. Finally, we introduce a jackknife procedure for bias reduction and a dynamic allocation scheme for improved efficiency.
Keywords: nested simulation, loss distribution, value-at-risk, expected shortfall, jackknife estimator, dynamic allocation.
Published in: Management Science, Vol. 56. No. 10, (October 2010), pp. 1833-1848.