Chapter 8

Risk and Summary Measures: Volatility and VaR

As argued in earlier chapters, risk measurement is the measurement of the profit and loss (P&L) distribution. This chapter introduces the standard quantitative techniques used to analyze the P&L distribution. By standard, I mean those most widely discussed in the literature and applied in the industry. In practice this means volatility and value at risk. Remember, however, that measuring risk is only the first step in managing risk, and there is more to measuring risk than just VaR.

Value at risk (usually referred to as VaR) is the most widely used and quoted quantitative risk measure. Much of this chapter focuses on introducing VaR and demystifying its uses and abuses. VaR, however, is only one measure among many that help to quantify and understand risk. Whatever tools we use, the important goal is to understand the distribution and potential variability of the P&L.

There are many good texts that cover VaR and quantitative risk measurement. Starting with the most nontechnical and intuitive, there is Crouhy, Galai, and Mark (2006) Chapter 7, and Crouhy, Galai, and Mark (2001) Chapter 5. Marrison (2002) has a concise introduction at the end of Chapter 5 and then devotes Chapter 6 to methods for VaR estimation. Jorion (2007) is a broad and detailed reference with Chapter 5 covering the basics, and additional topics such as the estimating and application of VaR covered throughout the book. McNeil, Frey, and Embrechts (2005) ...

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