Statistical modelling methods

We now investigate the possible use of statistical modelling in the hope that it might be more accurate than burn, and perhaps have other benefits too. We could, in principle, use a statistical model at any stage of the settlement process of a weather derivative. For example, for an HDD-based contract the settlement process consists of the following stages.

1. Collect daily Tmin and Tmax values.

2. Calculate Tavg.

3. Calculate daily HDD values.

4. Calculate the total HDD value.

5. Calculate the pay-off.

We could thus use a statistical model for any of the following.

1. Daily Tmin and Tmax.

2. Daily Tavg.

3. Daily HDD values.

4. The total HDD value.

5. The pay-off value.

We now discuss each of these in turn. The Tmin and Tmax time series could be modelled as stochastic time series. Looking at figure 1.1 we see that they show significant seasonal cycles in mean and variance, and correlations in time (autocorrelations). They are also cross-correlated at a range of lags. This is a hard statistical modelling problem, and a discussion of the methods that could be used is postponed until chapter 7. Tavg is simpler to model since there is now only one series, and hence no cross-correlations. But even modelling Tavg alone still turns out to be reasonably challenging because of the seasonality and autocorrelation of observed temperatures. Models for Tavg are considered in detail in chapter 6.