Analyses of chance occurrences: Professor Fred Espen Benth has developed entirely new mathematical models designed to calculate the optimal purchase and sale of weather and wind.
Photo: Yngve Vogt

Apollon research magazine interviews Professor Fred Espen Benth, Centre of Mathematics for Applications (CMA) at the University of Oslo in Norway. Such trading makes it possible to make money, or lose it, depending on whether it is too hot or cold, raining or snowing, explains the Professor. During recent years he has done research on how to earn money and acquire financial guarantees against bad weather.

Earlier Benth developed robust financial simulations aimed at increasing the understanding of risk in options trading such as the purchase and sale of electricity at fixed prices and at given points in time.

The purchase and sale of inclement weather is primarily associated with the electricity market. Electricity suppliers are fond of sub-zero temperatures as cold weather means that they make lots of money from the sale of electrical power.

On the other hand, they can incur large losses during warm winters. To ensure themselves against temperature fluctuations, power companies shop for so-called temperature variants on the exchange.

They can "exchange" varying temperatures with a fixed temperature. This can be compared with borrowing money at a fixed or floating interest rate.

Before the advent of stock exchanges it was possible to enter into similar contracts with insurance companies, but in contrast to insurance companies, there is no burden of proof required by the stock exchange. The high or low temperature level is proof enough, Bent says.

Storm shopping may also be interesting for airlines and large companies that stand to lose large sums of money due to bad weather. Schiphol Airport in Amsterdam purchases Frost Index products on Chicago Exchange.  Slippery runways entail extra expenses for both the airport and the airlines.

The storm market also attracts financial speculators and since the stock market obviously does not influence temperatures, one is able in this way to spread one's risk.

Mathematical models
There are great differences between weather derivatives and normal stocks. In the financial world, a stock is a stock regardless of how it is purchased. Weather derivatives, however, are different.

Imagine that a supplier of electricity in Copenhagen wants to buy temperature products in order to ensure the company against an excessively warm winter. There are no temperature derivatives for Copenhagen. The Chicago Exchange sells temperature derivatives for only 10 European cities, among them Oslo, Stockholm, Berlin and Amsterdam.

This means that the electricity supplier in Copenhagen has to purchase weather derivatives for other cities and balance them. An optimal solution might be to purchase a half derivative in Oslo, a quarter in Stockholm, and an eighth in Berlin with an eighth in Amsterdam.

Mathematicians call this balancing of weather derivatives "spatial financing."

Working with his wife, Jurate Saltyte Benth, who several years ago was a post-doctoral research fellow at the University of Oslo, Professor Benth developed new mathematical models for analysing weather derivatives in the market. 

These are statistical simulation models based on stochastic differential equations. (Stochastics is the exact science of chance occurrences). Differential equations are mathematical equations describing changes in time and space.

"This is the first time we bring spatial statistics into financial models. We put together a number of weather contracts and have optimised the model to achieve the least possible risk. These are entirely new stochastic models," says Benth.

Within the models seasonal variations have been incorporated throughout a year's time. It has been shown that uncertainty in the purchase and sale of weather derivatives is greater during summer and winter than spring and autumn.

"Our hope now is to obtain real financial data so that we can see if the model predicts correctly," says Benth.

Weather has a memory
In contrast to ordinary stocks, weather derivatives have a memory. If the market perceives that a company will become bankrupt in the near future, the share price will plunge towards zero straightaway. This is called a Markovian feature. This is not the case with weather.

If it is minus ten today, the probability is slight that it will be five degrees above zero tomorrow, even though there is no guarantee at all concerning the weather.

In the temperature market, one therefore sees uncertainty declines, just before the issuance of a temperature derivative. In the commodity market, the situation is the opposite. The same should hold true for the gas and electricity market, but  the same effect is not seen there.

"We have developed a new method based on an existing theory. The models have already created a stir internationally."

Benth does not know if  models have been implemented. There is a lot of financial secrecy in the private business world. "But of course those who use our model have an advantage," he says.

If everyone traded in the same way, all demand would be wiped out, but the need for weather shopping varies. Some use simple, others use more advanced models. Some speculate; some hedge against risks. Others go in when the volume is high, some choose to trade in low volumes.

 Purchase and sale of wind


Architect Chetwoods 'wind' dam uses a giant spinnaker sail slung between mountains to funnel wind into a turbine.

The sale of temperatures and precipitation is only the first step. Wind derivatives are next on the way targeting the windparks and farms. These need to ensure themselves against both the lack or excess of wind when mills grind to a halt. With small adjustments, Fred Espen Benth's financial model can also be used to analyse the purchase and sale of wind.

Below: Spatial variability, none of these are suitable for a robust financing report.