In chapter 4 we considered methods for the pricing of temperature-based weather derivatives that involve statistical modelling of the historical values of the contract settlement index. In this chapter we investigate methods that involve statistical modelling of the underlying temperature. Since the temperature measurements used for most weather contracts are daily values we will focus on the modelling of daily temperatures.

Using models of daily temperature to price weather derivatives has a number of advantages and disadvantages relative to using models of the contract settlement index.

The potential advantages include:

• more complete use of the available historical data;

• more accurate representation of the index distribution;

• more accurate extrapolation of extremes;

• more accurate mark to model estimates during the contract;

• consistent use of one model for all contracts on one location;

• easier incorporation of meteorological forecasts into the pricing algorithm.

The main disadvantage of using daily models is the added complexity; as we will see, daily models are significantly more complex than the index modelling methods of chapter 4. This, in turn, leads to greater risk of model error.

In practice, because of this disadvantage, daily models are currently used much less frequently than index models. However, as more research is done into these models their use is likely to increase.

The advantages of daily modelling

We now describe in more detail the advantages of using daily temperature modelling methods.