TABLE OF CONTENTS In this chapter, we discuss begin a discussion of VAR, an acronym for Value at Risk [i]. The "Plain-Vanilla VAR" (PV-VAR) along with its incarnation as a quadratic form ( QPV-VAR) is a standard risk measure that we discuss first. PV-VAR is rather blunt and unrefined [1]. In the next chapter, we will discuss refinements. The first refinement stage defines the "Improved Plain-Vanilla VAR" ( IPV-VAR). Further refinements produce the "Enhanced/Stressed VAR" ( ES-VAR) [2]. We give a few previews in the footnotes, which also contain other important points.
The various components of the VAR, called CVARs, will also be discussed. The CVARs are useful because they give a consistent picture of the composition of the risk. We show that the CVARs have uncertainties (i.e. there is a CVAR volatility) and we show how to calculate these uncertainties [3]. The CVAR volatility is useful because it shows the uncertainty in different possible compositions for a given total risk.
We first describe "Plain-Vanilla VAR" ( PV-VAR). Basically, PV-VAR is a one-step simulator in time that measures risks at a given confidence level of a portfolio [4] C using a variety of simplifying assumptions. The portfolio C is a function of underlying variables { x ?}. ? = 1 n. The variable x ? can be a physical variable (e.g. interest rate, stock price, etc.), or x ? can be a function,...
