164 THE MODELING OF WEATHER DERIVATIVE PORTFOLIO RISKone could transform to any other multivariate distribution, such as a multi-
variate t-distribution, or a multivariate non-parametric distribution. There
is no weather-derivative specific published work in this area, however, at
this point, and no evidence has been presented either for or against the
general validity of the Gaussian copula for weather indices (although one
would assume that there are probably cases where the Gaussian copula is
not a good model).
8.8 ESTIMATING MODEL ERROR
One of the biggest shortcomings of the BMVN method is that the results
may depend in a sensitive way on the assumptions in the method, and
the assumptions may be wrong. For comparison, analysis of the pricing
of single weather derivative contracts has shown that the results are very
sensitive to the choice of the numbers of years of historical data used and
the form of detrending, but less sensitive to the choice of distribution (see
Jewson (2004)). These results presumably carry over to the portfolio case.
This presents a serious problem for the risk manager: an apparently innocu-
ous decision to use 30 rather than 40 years of historical data may have a
large impact on the final results. What can be done about this? We offer two
approaches:
1 Run scenario tests on the assumptions used. By this we mean: vary each
assumption within a reasonable range, see how much the final results
change, and combine all the results together. For instance, repeat all cal-
culations with 40 rather than 30 years of data, with non-linear rather than
linear trends, with non-parametric rather than parametric distributions,
and with different estimators for the correlation matrix. The advantage of
this approach is that it is simple to do. The disadvantage is that it isad hoc,
and very subjective. Two different practitioners would vary different
sets of assumptions, and by different amounts, and would get different
results.2 Use a number of different models, with likelihood weighting (also called
“Bayesian Model Averaging”: see Hoeting, Madigan, Raftery and Volin-
sky, 1999). This is a slightly more formal version of the previous method
that avoids some of the subjectivity. This time, for each set of assump-
tions, we calculate the likelihood of the historical observations. Only the
sets of assumptions that give high values for the likelihood are retained,
and the final simulations are combined using the likelihood values for
each model. This method still involves some subjectivity in the definition
of the set of models to be considered, but avoids the ad-hockery in the
decision of how much each assumption should be varied.