In the absence of a clear and fundamental reason to select one set of seasons over another, the market seems to be moving to a consensus of using the recent one or two decades of data on which to base prices. Two decades does not contain enough information and is too small a sample size with which to calculate a valid volatility measure. In seeking an alternative, we search for corrective lenses through which to view history to make it useful for weather pricing.
Tucson temperature history is not flat making the data as measured troublesome for weather derivative pricing. We analyze temperatures and degree-days in Tucson to show this trend and to propose one alternative to "manage" it. We choose Tucson because it is actively traded in the over-the-counter (OTC) weather derivative market and it is among the cities for which the Chicago Mercantile Exchange may support weather futures contracts. It is a challenging location for a weather derivative analysis.
We deconstruct the past and reconstruct it - we build a "new" history. For Tucson, we reconstruct the full fifty years of history that would have occurred if the current population in Tucson today had been there for the full fifty of history.
We do this by fitting a polynomial to the time series of degree-days to quantify the trend. We then calculate the volatility of history about this trend. That is we calculate the departures of history from the running average of our trend, rather than from a fixed average. We then reconstruct history by choosing a level about which the adjusted historical volatility would have operated.
We use "Burn Analysis," probably the simplest method for modeling prices, to illustrate the impact on prices of "shaping history."