Acknowledgements

Certain sections of this chapter were drawn from Implementing Value at Risk, by
Philip Best, John Wiley, 1998. John Wiley’s permission to reproduce these sections
is kindly acknowledged.
The author would also like to thank Con Keating for his invaluable assistance in
reviewing this chapter and for writing the appendix on Extreme Value Theory. This
chapter also benefited from the comments of Gurpreet Dehal and Patricia Ladkin.

Notes
1 Note that observing other market parameters, such as the volatility of short-term interest
rates, might have warned the risk manager that a currency devaluation was possible.
Observed by a central risk management function in a different country, however, the chances
of spotting the danger are much reduced.
2 That is, twenty times the return volatility prior to the crisis.
3 Z score of binomial distribution of exceptions: 1.072, i.e. the VaR model would not be rejected
by a Type I error test.
4 Extreme price changes that have an almost infinitesimally small probability in a normal
distribution but which we know occur with far greater regularity in financial markets.
5 For a more comprehensive coverage of EVT see Embrechs et al. (1997).
6 This is the number of ways of selecting n assets from a set of 10, all multiplied by the
number of scenarios – 69 for this example.
7 Counterparty A’s liquidators would expect the bank to perform on the contracts, thus their
value at the time of default would have to be written off. Once written off, of course, there is
no potential for future beneficial market moves to improve the situation.
8 Bond price curvature – the slight non-linearity of bond prices for a given change in yield.
9 Note that this is not the same as the group of countries who have chosen to ‘peg’ their
currencies to the US dollar.
10 For a more formal and complete introduction to EVT see Embrechs et al. (1997), Reiss and
Thomas (1997) and Beirlant et al. (1996). Readers interested in either the rapidly developing
multivariate theory or available software should contact the author. 261