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

8.6 Uncertainty and Randomness—the Illusion of Certainty

Uncertainty and randomness enters all aspects of finance and enters into both the estimation and the use of volatility and VaR; the maxim that there is nothing certain but death and taxes is as true for VaR and volatility as for any aspect of finance. There is, however, a natural tendency to fall into an “illusion of certainty”; because we have measured the volatility or VaR, somehow the future has become less random. Much of the first section of this book focused on the notion that human intuition and our natural training often do not prepare us well to recognize and manage randomness.

Uncertainty and randomness will enter into quantitative risk measurement in a number of different ways:

First, any measurement, say of volatility or VaR, is an estimate, based in some manner on history and various assumptions. Like any estimate, it is subject to statistical uncertainty resulting from various sources, some easy to quantify, some impossible. Among the sources of uncertainty will be:

Measurement error, for example, if P&L is reported incorrectly, late, or not at all for some period or some portion of the portfolio

Finite data ...