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Glossary of Terms
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ARMA (see Autoregressive Models)
Autoregressive (AR) Models
Daily Simulation Models for temperature often rely in part on
autoregressive (AR) models. These are a subset of the class of
autoregressive-moving-average (ARMA) models. If we make the assumption
that there is a fixed seasonal cycle in the mean (and maybe the
variance) of temperature then the departures (or anomalies) from this
seasonal cycle can be modelled reasonably well as an AR process. In this
model the temperature anomaly today depends on a weighted sum of the
temperature on one or more previous days, plus some random variability.
In finance, the term ‘mean-reverting model’ is occasionally used to
refer to AR(1) models, that is, AR models which only use the previous
day’s value.
Average Temperature or (TAVG)
Many temperature related weather derivative contracts are based on
indices (commonly CDDs and HDDs) derived from daily values of Average
Temperature. Average Temperature is the mean of the minimum and maximum
daily temperatures, which are the parameters usually measured at
meteorological observing stations. Note that Tavg is not the same as the
mean temperature during the day, which is not usually measured.
Burn Analysis
Burn Analysis is the simplest form of weather derivative pricing. It
involves taking historical values for the index (which may be based on
raw, Cleaned, or Enhanced data, and which may have been detrended in
some way) and applying the financial contract to them. Depending on the
quality of the data used to calculate the historical indices used, Burn
Analysis may give a useful first indication of the mean and range of
possible payouts of a weather derivative contract, and can be done
simply in a spreadsheet. The disadvantages of Burn Analysis are that it
may not capture the possible extremes and may be unduly influenced by
individual years in the historical record. It can also not be extended
easily to analyse a portfolio of contracts.
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