Quantitative Risk Management: A Practical Guide to Financial Risk, + Website

5.4 Calculating Volatility and VaR

So far we have been talking about volatility, VaR, and the P&L distribution as if we already knew the distribution, as if somebody gave it to us. This is clearly not the case. We have to estimate them, and that is never easy.

I leave a detailed discussion of the topic to Chapters 8 and 9. It is important, however, to know some of the terms. There are three widely used methods for estimating volatility and VaR: parametric (also called linear, delta normal, or variance-covariance), historic simulation, and Monte Carlo. There are important differences between them and we discuss some of the pros and cons in Chapter 8 and run through an example in Chapter 9. For the moment, the similarities are more important.

Whatever approach we take, the P&L distribution is the fundamental entity. We may talk about volatility and VaR but these simply summarize the distribution itself. As always, it is good to recognize the modesty of our tools. We would like to know what the P&L distribution will be tomorrow, but that is a vain hope; we can only estimate what it was in the past and then assume or hope that it will be similar in the future. Nonetheless, understanding how the portfolio would have behaved is extremely informative and the first step toward understanding how it might behave going forward.

The goal of any approach for estimating the P&L distribution is to estimate how the current portfolio would have behaved under a variety of conditions, the conditions ...