Stress Testing a model/Backtesting

Discussion on Value-at-Risk Models
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Posts: 20
Joined: Sun Nov 16, 2008 10:07 am

Stress Testing a model/Backtesting

Postby FatTail » Fri Jul 24, 2009 2:36 pm


I am looking at producing a stressed result for a risk model.


- Assume using a simple risk model e.g. simple plain Hist Sim with 3year data window
- I would like to produce an indicator/estimate of how wrong it could be over next year

Potential approach I am thinking about
- take some key market data series over long time period e.g. 30 years USDJPY FX etc,
- declare what risk statistic I am concerned about e.g. STDEV of distribution
- For each day i starting after 3 years
- (a) calculate relevant risk statistic (eg STDEV) for the three year data window for day i (data widow 3 years before i)
- (b) calculate various samples of risk statistic (eg STDEV) of 1 year bootstrapped samples from same 3 year data window and divide these by (a) – then calculate percentiles for this ratio from the samples e.g. 90 % and 10 % from this for each day i
- (c) calculate risk statistic (eg STDEV) for 1 year data window after i and divide by (a)
- (d) repeat this for i+1 etc for next 26 years of data
- (e) this can then be shown as a graph with ratio (c) and percentile levels from (b)
- (f) also then count % of time the realised ratio is above/below the model implied percentages (will be a lot higher than 10%)
- (g) finally calculate how much would have to % increase the 90 % and 10 % on average to make above and below exceedences the right number

- Does this sound reasonable
- Is there a simpler better way to do this
- I have not calculated the ranges but have looked at (c) and the time series of it – that looks quite useful on its own, and then if I take the standard deviation of this series/ratio it seems quite an interesting statistic also (and could maybe be compared to what you get from Normal, fat tailed modelled dist)


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Joined: Sun Sep 28, 2008 10:30 pm

Re: Stress Testing a model/Backtesting

Postby coalexander » Mon Aug 17, 2009 1:14 pm


Apologies for the late reply, but I have been away for 3 weeks on holiday, recovering from a double bereavement. I am away next week also, on a family holiday.

Have you read Section IV.6.3.2 on distribution of VaR estimators in simulation models (and IV.6.3.1 on distribution of VaR estimators in parametric linear models)...? There you will find a much simpler analytic solution for the 'error' in a VaR estimator. I attach an extract to this message, and I hope this helps, Carol

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