Market Risk Modelling
First published:
ISBN: 9781906348779
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Fitting Probability Distributions to Data
Preface
Risk Modelling and its Myths
Mastering the R Statistical Package
Key Concepts on Probability
Tools for Describing Risk Factors and Portfolios
The Essentials of Hypothesis Testing for Risk Managers
Alternative Methods to Measure Correlation
A Primer On Maximum Likelihood Estimation
Regression in a Nutshell
Fitting Probability Distributions to Data
Practical Principal Components Analysis
Three Essential Models for Volatility
Random Numbers and Applied Simulation
Tail Risk Modelling
Conclusion to 'Market Risk Modelling (2nd edition)'
It is often necessary to fit probability distributions to risk factors and portfolios for descriptive, predictive or simulation purposes. For example, risk measures such as VaR often require the specification of a probability model for the return distribution. All the probability distributions listed in this chapter can be easily calculated in a spreadsheet without the need for any programming. I have found these distributions satisfy 95% of requirements when modelling continuous risk factors and portfolios.
UNDERSTANDING PROBABILITY DISTRIBUTIONS
Consider the problem of finding a suitable probability distribution for the log returns of the three-month forward price of zinc using a sample from January 5, 1998, to August 31, 2002. Our objective is to find the VaR0.95 of a US$25 million portfolio fully invested in zinc. Table 9.1 presents descriptive statistics for this asset. While there is a moderate degree of skew, it is the size of the relative kurtosis that is the key characteristic. The value of the 1st percentile of the data is – 2.485%, therefore VaR0.99 = US$621,250.
Table 9.1 Descriptive statistics for the three-month forward zinc log daily return
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