Fitting Probability Distributions to Data

Nigel Da Costa Lewis

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

Average

Sorry, our subscription options are not loading right now

Please try again later. Get in touch with our customer services team if this issue persists.

New to Risk.net? View our subscription options

You need to sign in to use this feature. If you don’t have a Risk.net account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an individual account here