**Weather derivatives** are financial instruments that can be used by organizations or individuals as part of a

risk managementRisk management is the identification, assessment, and prioritization of risks followed by coordinated and economical application of resources to minimize, monitor, and control the probability and/or impact of unfortunate events or to maximize the realization of opportunities...

strategy to reduce risk associated with adverse or unexpected weather conditions. The difference from other

derivativesA derivative instrument is a contract between two parties that specifies conditions—in particular, dates and the resulting values of the underlying variables—under which payments, or payoffs, are to be made between the parties.Under U.S...

is that the underlying asset (rain/temperature/snow) has no direct value to price the weather derivative.

## Overview of uses

Farmers can use weather derivatives to

hedgeA hedge is an investment position intended to offset potential losses that may be incurred by a companion investment.A hedge can be constructed from many types of financial instruments, including stocks, exchange-traded funds, insurance, forward contracts, swaps, options, many types of...

against poor harvests caused by drought or frost; theme parks may want to insure against rainy weekends during peak summer seasons; and gas and power companies may use

heating degree dayHeating degree day is a measurement designed to reflect the demand for energy needed to heat a home or business. It is derived from measurements of outside air temperature. The heating requirements for a given structure at a specific location are considered to be directly proportional to the...

s (HDD) or cooling degree days (CDD) contracts to smooth earnings. A sports event managing company may wish to hedge the loss by entering into a weather derivative contract because if it rains the day of the sporting event, fewer tickets will be sold.

Heating degree days are one of the most common types of weather derivative. Typical terms for an HDD contract could be: for the November to March period, for each day where the temperature rises above 18 degrees Celsius keep a cumulative count of the difference between 18 degrees and the average daily temperature. Depending upon whether the option is a

put optionA put or put option is a contract between two parties to exchange an asset, the underlying, at a specified price, the strike, by a predetermined date, the expiry or maturity...

or a

call optionA call option, often simply labeled a "call", is a financial contract between two parties, the buyer and the seller of this type of option. The buyer of the call option has the right, but not the obligation to buy an agreed quantity of a particular commodity or financial instrument from the seller...

, pay out a set amount per heating degree day that the actual count differs from the strike.

## History

The first weather derivative deal was in July 1996 when Aquila Energy structured a dual-commodity hedge for Consolidated Edison Co. The transaction involved ConEd's purchase of electric power from Aquila for the month of August. The price of the power was agreed to, but a weather clause was embedded into the contract. This clause stipulated that Aquila would pay ConEd a rebate if August turned out to be cooler than expected. The measurement of this was referenced to Cooling Degree Days measured at New York City's Central Park weather station. If total CDDs were from 0 to 10% below the expected 320, the company received no discount to the power price, but if total CDDs were 11 to 20% below normal, Con Ed would receive a $16,000 discount. Other discounted levels were worked in for even greater departures from normal.

After that humble beginning, weather derivatives slowly began trading over-the-counter in 1997. As the market for these products grew, the

Chicago Mercantile ExchangeThe Chicago Mercantile Exchange is an American financial and commodity derivative exchange based in Chicago. The CME was founded in 1898 as the Chicago Butter and Egg Board. Originally, the exchange was a non-profit organization...

introduced the first exchange-traded weather futures contracts (and corresponding options), in 1999. The CME currently trades weather derivative contracts for 18 cities in the United States, nine in Europe, six in Canada and two in Japan. Most of these contracts track cooling degree days or heating degree days, but recent additions track frost days in the Netherlands and monthly/seasonal snowfall in Boston and New York. A major early pioneer in weather derivatives was

EnronEnron Corporation was an American energy, commodities, and services company based in Houston, Texas. Before its bankruptcy on December 2, 2001, Enron employed approximately 22,000 staff and was one of the world's leading electricity, natural gas, communications, and pulp and paper companies, with...

Corporation, through its EnronOnline unit.

In an Opalesque video interview, Nephila Capital's

Barney Schauble discusses how some hedge funds have now begun focusing on weather derivatives as an investment class. Counterparties such as utilities, farming conglomerates, individual companies and insurance companies are essentially looking to hedge their exposure through weather derivatives, and funds have become a sophisticated partner in providing this protection. There has also been a shift over the last few years from primarily fund of funds investment in weather risk, to more direct investment for investors looking for non-correlated items for their portfolio. Weather derivatives provide a pure non-correlated alternative to traditional financial markets.

## Valuation

There is no standard model for valuing weather derivatives similar to the Black-Scholes formula for pricing European style equity option and similar derivatives. That is due to the fact that underlying asset of the weather derivative is non-tradeable which violates a number of key assumptions of the BS Model. Typically weather derivatives are priced in a number of ways:

### Business pricing

Business pricing requires the company utilizing weather derivative instruments to understand how its financial performance is affected by adverse weather conditions across variety of outcomes (i.e. obtain a utility curve with respect to particular weather variables). Then the user can determine how much he is willing to pay in order to protect his/her business from those conditions in case they occurred based on his/her cost-benefit analysis and appetite for risk. In this way a business can obtain a 'guaranteed weather' for the period in question, largely reducing the expenses/revenue variations due to weather.

Alternatively, an investor seeking certain level or return for certain level of risk can determine what price he is willing to pay for bearing particular outcome risk related to a particular weather instrument.

### Historical pricing (Burn analysis)

The historical payout of the derivative is computed to find the expectation. The method is very quick and simple, but does not produce reliable estimates and could be used only as a rough guideline. It does not incorporate variety of statistical and physical features characteristic of the weather system.

### Index modelling

This approach requires building a model of the underlying index, i.e. the one upon which the derivative value is determined (for example monthly/seasonal cummulative

heating degree dayHeating degree day is a measurement designed to reflect the demand for energy needed to heat a home or business. It is derived from measurements of outside air temperature. The heating requirements for a given structure at a specific location are considered to be directly proportional to the...

s). The simplest way to model the index is just to model the distribution of historical index outcomes. We can adopt

parametricParametric statistics is a branch of statistics that assumes that the data has come from a type of probability distribution and makes inferences about the parameters of the distribution. Most well-known elementary statistical methods are parametric....

or

non-parametric distributionsIn statistics, the term non-parametric statistics has at least two different meanings:The first meaning of non-parametric covers techniques that do not rely on data belonging to any particular distribution. These include, among others:...

. For monthly cooling and heating degree days assuming a

normal distribution is usually warranted. The predictive power of such model is rather limited. A better result can be obtained by modelling the index generating process on a finer scale. In the case of temperature contracts a model of the daily average (or min and max) temperature time series can be built. The daily temperature (or rain, snow, wind, etc.) model can be built using common statistical

time seriesIn statistics, signal processing, econometrics and mathematical finance, a time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones index or the annual flow volume of the...

models (i.e.

ARMAIn statistics and signal processing, autoregressive–moving-average models, sometimes called Box–Jenkins models after the iterative Box–Jenkins methodology usually used to estimate them, are typically applied to autocorrelated time series data.Given a time series of data Xt, the ARMA model is a...

or

Fourier transformIn mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...

in the frequency domain) purely based only on the features displayed in the historical time series of the index. A more sophisticated approach is to incorporate some physical intuition/relationships into our statistical models based on spatial and temporal correlation between weather occurring in various parts of the ocean-atmosphere system around the world (for example we can incorporate the effects of

El NiñoEl Niño/La Niña-Southern Oscillation, or ENSO, is a quasiperiodic climate pattern that occurs across the tropical Pacific Ocean roughly every five years...

on temperatures and rainfall).

### Physical models of the weather

We can utilize the output of

numerical weather predictionNumerical weather prediction uses mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions. Though first attempted in the 1920s, it was not until the advent of computer simulation in the 1950s that numerical weather predictions produced realistic...

models based on physical equation describing relationships in the weather system. Their predictive power tends to be less or similar to purely statistical models beyond time horizons of 10–15 days.

Ensemble forecastsEnsemble forecasting is a numerical prediction method that is used to attempt to generate a representative sample of the possible future states of a dynamical system...

are especially appropriate for weather derivative pricing within the contract period of a monthly temperature derivative. However, individuals members of the ensemble need to be 'dressed' (for example with gaussian kernels estimated from historical performance) before a reasonable probabilistic forecast can be obtained.

### Mixture of statistical and physical models

A superior approach for modelling daily or monthly weather variable time series is to combine statistical and physical weather models using time-horizon varying weight which are obtained after optimization of those based on historical out-of-sample evaluation of the combined model scheme performance.

## Further reading

- Considine, G., 2000, "Introduction to Weather Derivatives", Weather Derivatives Group, Aquila Energy.
- Peter Robison, "Hedge Funds Pluck Money From Air in $19 Billion Weather Gamble",
*Bloomberg News*, August 2, 2007.
- USA Today (2008), "Weather Derivatives becoming hot commodities", USA Today Online posted 6/9/2008.
- Alice Gomstyn, Rich Blake and Dalia Fahmy, "Want a Weather Forecast? Ask Wall Street"
*ABC News*, February 8, 2010.
- Dischel, R. S., Ed. (2002). "Climate Risk and the Weather Market: Financial Risk Management with Weather Hedges", Risk Books.
- Jewson, S., A. Brix and C. Ziehmann (2005). "Weather Derivatives Valuation: The Meteorological, Statistical, Financial and Mathematical Foundations". Cambridge, Cambridge University Press.
- Golden, L. L., M. Wang and C. C. Yang "Handling Weather Related Risks Through the Financial Markets: Considerations of Credit Risk, Basis Risk, and Hedging." Journal of Risk & Insurance, Vol. 74, No. 2, pp. 319–346, June 2007.
- Myers, R. 2008 "What Every CFO Needs to Know About Weather Risk Management", Storm Exchange, Inc. & CME Group
- Mathews, J. S. (2009) "Dog Days and Degree Days", CME Group
- Tang, K., Ed. (2010). "Weather Risk Management: A guide for Corporations, Hedge Funds and Investors", Risk Books.

## See also

- Weather Risk Management
Weather risk management is a type of risk management done by organizations to address potential financial losses caused by unusual weather.-Overview:...

- MSI GuaranteedWeather, LLC
MSI GuaranteedWeather, LLC is a weather risk management company based in Overland Park, Kansas. It began in 1999 as a subsidiary of Aquila, Inc. but since 2007 is a wholly owned subsidiary of Mitsui Sumitomo Insurance Co., Ltd.- External links :* *...

- Weatherbill
WeatherBill is an online service, launched in January 2007, that helps people and businesses adapt to climate change. The company’s technology platform enables the real-time pricing and purchasing of customizable weather insurance using proprietary global weather simulation modeling and local...

- Alternative Risk Transfer
Alternative Risk Transfer is the use of techniques other than traditional insurance and reinsurance to provide risk bearing entities with coverage or protection...

- Fixed bill
Fixed Bill refers to an energy pricing program in which a consumer pays a predetermined amount for their total energy consumption for a given period. The price is independent of the amount of energy the customer uses or the unit price of the energy...

- CelsiusPro
CelsiusPro AG is a Swiss company specialized in structuring and originating OTC weather derivatives worldwide. Using a proprietary platform, CelsiusPro enables online price calculation, execution and position reporting as well as weather statistics and analysis...

## External links