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I need to create a loss distribution for a credit portfolio as the first steps to estimate the portfolio Credit VaR.

I have historical monthly account snapshots (payment history) of all accounts going back 5 years. I need a simple intuitive approach.

I will assume that defaults are uncorrelated and also the recovery rate for all defaulted loans is same (x%)

I am thinking of below steps:

-Pick a vintage- Say Jan 2015.i.e the population to study is all loans opened in Jan 2015.
-For each loan in above, see how many defaulted within 12 months of origination. Say p%
-Assume a standard recovery rate (x%) for defaulted loans.
-Loss of this particular vintage within 1 year = Sum(pxindividual loan balance at default)

Now I repeat the calculation selecting a different vintage..i.e loans originated in Feb 2015. I have 5 years(60 months), so I will have 60 different values of expected loss. Using this, if I draw a histogram , where the x axis represents different values of the EL and y axis the relative frequency of that particular loss, I have a probability density function. Can this be used as a loss distribution?

If yes, I can proceed to calculate the x value corresponding to the 5% significance level and that will be my VaR, correct?

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It would indeed provide a QD empirical loss density, though a few problems. The default rates would have autocorrelation due to the use of the monthly snapshots (overlapping outcomes). Last 60 months data probably won’t capture extreme loss events so extreme quantiles will be inaccurate. Another subtle point is around the economic cycle, as you would have noticed, good and bad years are clustered due to the very nature of economic cycles, which will bring in additional correlation.

You can also try Vasicek loss distribution. Calibration of whose parameters such as the correlation and PD can be done using historical data and you will then get a much smoother loss distribution. Again the length of data and the autocorrelation etc will have an impact but at least you can then do some additional sensitivity analysis.

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  • $\begingroup$ Thank you, I will look into Vasicek. Can you elaborate about the auto-correlation? I understand individual defaults may be correlated to each other in a single point in time(i.e if a whole sector goes down), but not able to see the autocorrelation intuitively. $\endgroup$ – Victor123 Apr 22 at 19:19
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    $\begingroup$ Not proposing that you must read this article but the free summary should give you an idea of what I meant by autocorrelation in the default series: risk.net/journal-of-credit-risk/5429256/… $\endgroup$ – Magic is in the chain Apr 22 at 19:26

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