Bubble Value at Risk: A Countercyclical Risk Management Approach, Revised Edition

Chapter 5

Advanced VaR Methods

In this chapter, we will explore some advanced VaR models; there are many others.1 Academics were the first to systematically catalog the weaknesses of VaR and improve the basic VaR model in order to make it consistent with observed market behaviors. Unfortunately, the added layer of mathematical complexity makes implementation and common understanding difficult. As such, these models are slow in gaining industry acceptance.

One common trait of these models is the reliance on a strong mathematical foundation and its basic assumptions such as stationarity and being independent and identically distributed (i.i.d.). We will introduce the main ideas of these models without delving into the mathematical details as far as possible. Our goal is to cover just enough ground to be able to illustrate a simple example on a spreadsheet.

5.1 HYBRID HISTORICAL SIMULATION VaR

It is important for hsVaR to use an observation period long enough for the shape of the return distribution to be well-captured. But because hsVaR uses a rolling history of empirical data, it encounters a dilemma when estimating the quantile—with a long history the method becomes insensitive to market changes,2 while with a short history it encounters estimation problems—there are too few data points that define the quantile. The RiskMetrics version of pVaR on the other hand is very sensitive to market innovation, because of the use of exponentially declining weights on past data to estimate ...