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

Jamshidian and Zhu (1997) propose a discrete grid method for simplifying the computation of Value at Risk (VaR) for fixed-income portfolios. 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, they use a discrete approximation to the distribution of the portfolio's value. We show that their method has two serious shortcomings which 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. We propose two refinements to their method to correct these two shortcomings. First, we propose choosing risk factors according to their ability to explain the portfolio's value. To do this, instead of generating risk factors with principal components analysis, we generate them with a statistical technique called partial least squares. Second, we compute VaR with a ``Grid Monte Carlo'' method that uses continuous risk factor distributions while maintaining the computational simplicity of a grid method for pricing. We illustrate our points with several example portfolios where the Jamshidian-Zhu method fails to accurately estimate VaR, while our refinements succeed.