By Kevin Dowd
This publication presents an advent to price in danger (VaR) and anticipated tail loss (ETL) estimation and is a student-oriented model of Measuring industry Risk (John Wiley & Sons 2002).
An creation to industry possibility Measurement contains insurance of:
- Parametric and non-parametric danger estimation
- Numerical tools
- Liquidity hazards
- Risk Decomposition and Budgeting
- Stress trying out
- Model possibility
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Additional resources for An introduction to market risk measurement
These are serious criticisms, and they are not easy to counter. Another problem was pointed out by Ju and Pearson (1999): if VaR measures are used to control or remunerate risk taking, traders will have an incentive to seek out positions where risk is over- or underestimated and trade them. They will therefore take on more risk than suggested by VaR estimates — so our VaR estimates will be biased downwards — and their empirical evidence suggests that the magnitude of these underestimates can be very substantial.
18 An Introduction to Market Risk Measurement A more general approach to dispersion is provided by Fishburn α − t measures, deﬁned as (t − x)α f (x) dx (Fishburn (1977)). This measure is deﬁned on two parameters: α, which describes our attitude to risk, and t, which speciﬁes the cut-off between the downside that we worry about and other outcomes that we don’t worry about. Many risk measures are special cases of the Fishburn measure or are closely related to it. These includes the downside semivariance, which is very closely related to the Fishburn measure with α = 2 and t equal to the mean; Roy’s safety-ﬁrst criterion, where α → 0; and the expected tail loss (ETL), which is closely related to the Fishburn measure with α = 1.
The spread of the probability mass around the mean depends on the standard deviation σ : the greater the standard deviation, the more dispersed the probability mass. The pdf is also symmetric around the mean: X is as likely to take a particular value x − µ as to take the corresponding negative value −(x − µ). Outcomes well away from the mean are very unlikely, and the pdf tails away on both sides: the left-hand tail corresponds to extremely low realisations of the random variable, and the righthand tail to extremely high realisations of it.