Risk-Managing the Uncertainty in VAR Parameters

Managing risk successfully requires a detailed understanding of the distributions from which random shocks to asset prices are drawn. However, there is uncertainty in both the actual distribution of returns and the parameters characterizing the distribution. In this chapter, we focus on the uncertainty in estimating the distributional parameters, and how this uncertainty impacts value at risk calculations. We illustrate some traditional (but naïve) methods for handling parameter uncertainty and show that these methods could often lead to poor risk management results. We then provide techniques for quantifying risk more accurately when distribution parameters are estimated with low precision or when there are disagreements over the parameter estimates