A backtesting procedure compares the VaR prediction with the observed loss.
In a mark-to-model backtesting the observed loss is determined by
calculation of the present value before and after consideration of the
actually observed risk factor changes.
For
the present value at time
is calculated with the yield
, which is obtained from observed data for
by linear interpolation, according to
The different frameworks for the VaR estimation can easily be integrated into
the backtesting procedure.
When we, e.g., only consider changes of the benchmark curve,
in (3.23) is replaced with
.
On an average
per cent of the observed losses
in a given time interval should exceed the corresponding VaR (outliers).
Thus, the percentage of observed losses is a measure for the
predictive power of historical simulation.