Weather Derivatives: Instruments and
Pricing Issues
Mark Garman1, Carlos Blanco2 and Robert Erickson3
Article published in Environmetal Finance under the title “Seeking a Standard Pricing Model”自考英语本科科目
comforter,Environmental Finance, March 2000
Note: We would like to thank Angelo Barbieri, Director of Financial Engineering at FEA, and Michael Pierce, financial engineer at FEA, who contribution has been esntial for the development of the Weather Derivatives Pricing Models.
Introduction:
Since the summer of 1997, when the first weather derivatives transaction was recorded, we have witnesd the development of a new derivatives market in the United States, which is gradually expanding across the globe. The US Energy Department estimates that US$1 trillion of the US economy is expod to weather risk. So far, the notional size of the weather derivatives traded is around US$3.5 billion, which reprents a small amount compared with the size of the exposure.
el什么意思The main players in the weather derivatives markets can be grouped in four main categories: Market Makers, Brokers, Insurance and Reinsurance Companies, and End-Urs such as Gas and Power Marketers, Utilities and perhaps other market participants from retail, agriculture, travel, transport and distribution, leisure and tourism firms.
A derivative is a contract or curity who payoffs depend upon the price of some more fundamental, or “underlying” ast price. Derivatives are ud to control the risks of naturally-arising exposures to such an ast price. For example, a gold miner might undertake the sales of gold future contracts (a derivative providing for the future exchange of money and gold) to diminish his natural exposures to the price of gold inherent in the ownership of the gold mine, i.e. its future gold production. In the weather ca, the revenues of, for example, a ski slope operator, might reflect inherent weather risks which the operator may wish to mitigate via weather derivatives. For this purpo, the weather must be measured in some quantitative fashion, just like the price of gold.
Weather Measures
Just as an option on a commodity has as its underlying ast the price of a futures contract, a weather derivative has as its underlying “ast”, a weather measure. The type of measure depends
on the specifics of the contract. Most weather derivatives are bad on Heating Degree Days (HDD) or Cooling Degree Days (CDD). Other contracts are bad on precipitation, measured by the amount of rain over a given time period, or snowfall, measured by the amount of snow (including sleet) in a given period of time. However, it is estimated that 98-99% of the weather derivatives now traded are bad on temperature.
HDD and CDD
Intuitively, HDD and CDD measure the heating and cooling demands that ari by departures of average daily temperatures from a ba level.
1 Mark Garman is President for Financial Engineering Associates.
2 Carlos Blanco is Manager of Global Support and Educational Services for FEA.
3 Robert Erickson is Senior Financial Engineer for FEA.
An HDD is the number of degrees by which the day's average temperature is below a ba temperature, while a CDD is the number of degrees by which the day's average temperature is above a ba temperature. HDD and CDD are calculated as follows:
Daily HDD = Max (0, ba temperature – daily average temperature)
Daily CDD = Max (0, daily average temperature – ba temperature)
厚脸皮英语Ba temperature is the pre-specified “ba” temperature (usually 65 degrees Fahrenheit, but sometimes 75 in warmer climates). The daily average temperature is measured as the average between the daily high and daily low.
HDDs and CDDs are usually accumulated over a period of time. The most common derivative structures are bad on the cumulative HDDs or CDDs for one month or one ason (e.g. November to March). To calculate the HDD (CDD) over a period of days, we simply add up the daily HDD’s (CDD’s) for the period.
Occasionally other measures are ud in weather derivatives: For example, Energy Degree Days are the sum of HDD or CDD for each day Growing Degree Days (GDDs) are ud in agriculture, and are defined as the degrees between a certain range (e.g. between 55 and 75 degrees Fahrenheit).
Weather Derivatives Structures
The list of actual contracts in u is extensive and constantly evolving. Most of the weather derivatives traded up to date have been swaps and put or call options or combinations of the. In recent months, the weather derivatives market is starting to e customized structures for specific needs, such as binary or digital options, which either pay a fixed sum or zero depending on whether the payoff is satisfied, and double-trigger options, which pay off only if two conditions are met.
trizPayoffs are usually defined as a specified dollar amount (e.g. $1000 per degree day) multiplied by differences between the “strike” HDD (CDD) level specified in the contract and the actual cumulative HDD (CDD) level which occurred during the contract period.
In order to limit the maximum payout by any of the counterparties, the contracts are usually "capped," i.e. only a maximum amount of payout can change hands.
Call and Put Options Weather derivatives typically have as their underlying “ast” either HDDs or CDDs.
However, since weather is not in fact a tradable ast, a dollar amount is associated with every degree day in the payoff calculation. For example, consider a CDD call option with a strike of 1000 CDD’s paying $5000 per degree-day. The payoff for this option is:
()
1000,05000$|−×=T t CDD Max Call Payoff
where CDD t|T is the cumulative cooling degree days over the life of the contract. More generally, we can reprent the payoffs of the weather puts and calls as:
()
immortal()T t T t X K Max DD p Put Payoff K X Max DD p Call Payoff ||,0)/($:,0)/($:−×−× where p ($/DD) is the per degree day payoff, X t|T is the underlying (CDD or HDD), and K is the strike
(denominated in terms of the associated underlying measure).
An investor who is long (has purchad) a call option will receive the payoff if the recorded HDD or CDD for the ason are greater than the Strike K. An investor who is long the put will receive the payoff if the HDD or CDD for the ason are lower than the strike.
g7是什么意思
Call and Put Options with a Maximum Payoff (CAP) In order to avoid excessive payouts on the contracts due to extreme weather, the options often come with a cap or maximum payoff.
{}()
h K X Max DD p Min Call Payoff T t ,,0)/($ :|−× {}()h X K Max DD p Min Put Payoff T
t ,,0)/($ :|−×
where h is the maximum payoff denominated in dollars.
{}()h X K Max DD p Min Put Payoff T t ,,0)/($ :|−×
Example of a Weather derivatives trader's pricing sheet
Degree Option Bid Offer $DD CAP Location
WBAN Days Term Strike Type ($000) ($000) $ Millions Las Vegas 23,169 CDD May-Oct 3210
Call 260 300 5,000
1 Philadelphia 13,739
CDD Aug 370 Call 115 125 5,000 1 Weather Swaps A swap is a combination of a call and put option with the same strike and on the same underlying location. Degree day swaps can provide revenue stability. The payoff is:
{}(){}()
h X K Max DD p Min h K X Max DD p Min T t T t ,,0)/($,,0)/($ ||−×−−×
An investor who is long the swap will receive payments if the recorded HDD or CDD are greater than the strike, and will make payments if the recorded HDDs or CDDs are lower than the strike.
Collars or "fences"
Another spread position, a “collar,” insulates the buyer from extreme movements in the underlying ast.
A collar typically consists of purchasing an OTM put (call) with a particular strike, and financing this with the sale of an OTM call (put) with a different strike. The general payoff is:
{}(){}()
h X K Max DD p Min h K X Max DD p Min T t T t ,,0)/($,,0)/($ |21|−×−−× Payoff of a Collar (Short Put Strike =900; Long Call Strike = 1100-1250000-1000000
-750000
英语培训价格迈格森
-500000
-250000
250000500000
750000
1000000
1250000
Weather Derivatives Pricing Issues
RECENT MARKET DEVELOPMENTS
Weather derivatives markets have traditionally been characterized as having a small number of participants and large bid-ask spreads, but this is rapidly changing. During the last 18 months, the market has incread dramatically, and in the first mester of 1999 it is estimated that 800-1800 transactions have taken place in the United States, which reprent a sharp increa from 100-150 transactions in 1997.
In the following table we can e the measuring stations and the ticker symbols of the futures contracts traded in the Chicago Mercantile Exchange.
PRICING MODELS FOR WEATHER DERIVATIVES
There are different ways to price weather derivatives. Before using any approach, it is important to the gain an intuitive understanding and make sure that the model is accurately capturing reality.
There are some pricing models that focus on the HDD or CDD directly, while others attempt to model temperature directly, and then extract the HDD or CDD for each temperature scenario. We think that modelling temperature directly is a substantially better approach. The problem with modelling HDD o
r CDD directly as a normal or lognormal process is that after we calculate the weather measures, a lot of information is lost (since, among other things, HDD and CDD are bound by zero).
In the following example, we can e a extreme example of what could happen if we model only degree days instead of temperature. Two cities with very different temperatures could have the same number of degree days.
Location A 1-Jan 2-Jan 3-Jan Total HDD
1995 67 68 66 0
1996 65 55 65 10
blackout1997 65 66 68 0
Location B 1-Jan 2-Jan 3-Jan Total HDD
1995 85 83 81 0
1996 60 60 65 10
1997 79 81 80 0
Distribution of Weather Data; Trends and Seasonalities in Weather and choice of "Lookback Period".qihuang
Financial contracts derived from weather-specific measures, such as the expected future value of a local temperature, require the ability to predict regional weather conditions, months into the future. Thus, an
