Improving grid-based methods for estimating value-at-risk of fixed-income portfolios

Michael S. Gibson and Matthew Pritsker

Abstract

ABSTRACT

A discrete grid method for simplifying the computation of value-at-risk (VaR) for fixed-income portfolios was proposed by Jamshidian and Zhu (I 997). Their method relies on two simplifications. First, the value of fixed-income instruments is modeled as depending on a small number of risk factors chosen using principal components analysis. Second, a discrete approximation is used for the distribution of the portfolio's value. In this paper, it is shown that their method has two serious shortcomings that imply it cannot accurately estimate VaR for some fixed-income portfolios. First, risk factors chosen using principal components analysis will explain the variation in the yield curve, but they may not explain the variation in the portfolio's value. This will be especially problematic for portfolios that are hedged. Second, their discrete distribution of portfolio value can be a poor approximation to the true continuous distribution. The present authors suggest two refinements to correct these two shortcomings. First, it is proposed that risk factors be chosen according to their ability to explain the portfolio's value. To do this, instead of generating risk factors with principal components analysis, they are generated with a statistical technique called partial least squares. Second, VaR is computed with a "Grid Monte Carlo" method that uses continuous risk factor distributions while maintaining the computational simplicity of a grid method for pricing. Several example portfolios are presented for which the Jamshidian-Zhu method fails to estimate VaR accurately, while the proposed refinements succeed.