Weather Derivatives and Weather Risk Management

C© Risk Management and Insurance Review, 2005, Vol. 8, No. 1, 127-140

PERSPECTIVES

WEATHER DERIVATIVES AND WEATHERRISK MANAGEMENTPatrick L. BrockettMulong WangChuanhou Yang

ABSTRACT

Weather derivatives are a relatively recent kind of financial product developedto manage weather risks, and currently the weather derivatives market is thefastest-growing derivative market. The development of weather derivatives rep-resents one of the recent trends toward the convergence of insurance and finance.This article presents an overview of weather risks, weather derivatives, and theweather derivatives market, and examines the valuation of weather derivativesin an incomplete market, the hedging effectiveness of standardized weatherderivatives, as well as optimal weather hedging with the consideration of basisrisk and credit risk.

INTRODUCTION

Weather derivatives, which first emerged in the United States in 1997 following the dereg-ulation of American energy and power industries, represent a recent type of financialproduct developed to hedge weather risks. Global businesses are considerably exposedto increasingly uncertain global weather conditions. Besides energy and power indus-tries, agriculture, insurance, tourism, and retail businesses are also directly or indirectlyaffected by weather (see, for example, Dischel, 1998; Zeng, 2000). Weather derivativesenable those businesses that are adversely affected by unanticipated weather swingsto manage this risk, in the same way that hedgers regularly use traditional financialderivatives to hedge their risks in interest rates, equities, and foreign exchange.

According to the Chicago Mercantile Exchange (CME), the weather derivatives marketis the fastest-growing derivative market today.1 However, there are few studies thatdiscuss the key factors affecting the development of this evolving market. This article

Patrick Brockett is with the Red McCombs School of Business, University of Texas at Austin.Mulong Wang is at the College of Business Administration, University of Rhode Island. ChuanhouYang is at the Dahlkemper School of Business, Gannon University. This article was subject toanonymous peer review.The authors wish to thank the editors and the anonymous referees for their helpful comments onthis article.1 See Weather Products, Chicago Mercantile Exchange, at http://www.cme.com/prd/wec/

abtwthder2766.html.

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aims to fill this gap in the literature. Specifically, the article presents an overview ofweather risks, weather derivatives, and the weather derivatives market, and then exam-ines the valuation issue of weather derivatives in the incomplete market, the hedgingeffectiveness of standardized weather derivatives, as well as optimal weather hedgingwith consideration of basis risk and credit risk.

The article is structured as follows: The second section introduces weather risks andweather derivatives. The next section presents the development of the weather deriva-tives market. This is followed by sections investigating and summarizing current re-search on weather derivatives and weather hedging, and the last section concludes witha short summary and some ideas for future work.

WEATHER RISKS AND WEATHER DERIVATIVES

Weather risks are the uncertainty in cash flows and earnings caused by noncatastrophicweather events such as temperature, humidity, rainfall, snowfall, stream flow, and wind.They are contrasted with the catastrophe-related risks (CAT risks) caused by hurricanes,tornadoes, and windstorms, among others. Weather risks have an enormous impact onbusiness activities of many kinds. The U.S. Department of Commerce estimates thatnearly one third of the U.S. economy is directly affected by the weather.2 An article inthe New York Times (June 27, 1999) reports that American companies with significantexposures to weather risks have more than $1 trillion in yearly revenues. Similarly,an estimated $1.25 trillion of the European economy and $700 billion of the Japaneseeconomy are exposed to weather risks. A sample of weather risks faced by variousindustries is given in Table 1.

Weather exposure can be defined as dR/dW, i.e., the sensitivity of revenue (or cost) toweather indexes. However, weather risk is primarily considered as a volume or quantityrisk3 rather than a price risk. Although risk management tools for hedging price risks arewidely available, such instruments have limited applicability for hedging volume risk.To hedge volume risks caused by weather events (weather risks), weather derivativeshave been developed; they provide important complements to instruments that are bettersuited for hedging price risk.4 Weather derivatives differ from conventional derivativesin that there is no original and negotiable underlying index, which usually forms thebasis of a traditional derivative contract. Whereas financial derivatives are based on shareprices, bonds, exchange rates, or currencies, the underlying index of a weather derivativedefines the measure of weather conditions. The most common weather derivatives arebased on temperature changes. The underlying indexes are typically heating degreedays (HDDs) and cooling degree days (CDDs). A degree day is the measure of howmuch a day’s average temperature deviates from 65◦F. A Heating Degree Day (HDD)

2 See GuaranteedWeather at http://www.guaranteedweather.com. GuaranteedWeather is aglobal weather risk management company that manages an active portfolio of risk through-out the world.

3 Volume/quantity risk: risk that results from a change in the demand for goods due to a changein weather.

4 Weather derivatives are designed to hedge quantity risks (Muller and Grandi, 2000), but weatherderivatives can also be used as a “dirty hedge” of price risk if the correlation between price andweather index is not 0. A dirty hedge occurs when a derivative security cannot be fully hedgedwith liquid exchange-traded securities and/or its risk exposure changes over time or in responseto changes in a secondary underlying variable.

WEATHER DERIVATIVES AND WEATHER RISK MANAGEMENT 129

TABLE 1Illustrative Links Between Weather Indexes and Financial Risks

Risk Holder Weather Type Risk

Energy industry Temperature Lower sales during warm wintersor cool summers

Energy consumers Temperature Higher heating/cooling costsduring cold winters and hotsummers

Beverage producers Temperature Lower sales during cool summers

Building material companies Temperature/Snowfall Lower sales during severe winters(construction sites shut down)

Construction companies Temperature/Snowfall Delays in meeting schedulesduring periods of poor weather

Ski resorts Snowfall Lower revenue during winterswith below-average snowfall

Agricultural industry Temperature/Snowfall Significant crop losses due toextreme temperatures or rainfall

Municipal governments Snowfall Higher snow removal costs duringwinters with above-averagesnowfall

Road salt companies Snowfall Lower revenues during lowsnowfall winters

Hydroelectric power generation Precipitation Lower revenue during periodsof drought

Source: Climetrix, Risk Management Solutions Inc.5

measures the coldness of the daily temperature compared to a standard of 65◦F, whilea Cooling Degree Day (CDD) measures the warmth of the daily temperature comparedto the standard of 65◦F.6 The most common terms in the weather derivatives market areNovember 1 through March 31 for winter season contracts and May 1 through September30 for summer contracts.7 However, there is an increasing volume of trading in monthly,weekly, and multiyear contracts as the market grows.8

Currently, most weather derivatives are privately negotiated over-the-counter (OTC)contracts (see Climetrix at www.climetrix.com). OTC weather derivatives are usu-ally structured as call/put options and swaps based on different underlying weather

5 Risk Management Solution Inc. (RMS) (http:/www.rms.com) is the world’s leading provider ofproducts and services for the quantification and management of natural hazard risks. Climetrix(http://www.climetrix.com) is the weather team of RMS.

6 Daily HDD = Max (0, 65◦F – daily average temperature), and Daily CDD = Max (0, dailyaverage temperature – 65◦F). Weather derivatives are based on the accumulation of HDDs orCDDs during a certain period (contract period). To calculate the degree days over a period, thedaily degree days for each day in that period are simply aggregated.

7 April and October are often referred to as shoulder months.8 See Climetrix, RMS, Inc. at http://www.climetrix.com.


indexes. In addition to a number of electronic weather marketplaces (for example, In-tercontinental Exchange and Swiss Re’s ELRiX), two exchanges—CME (the ChicagoMercantile Exchange) and LIFFE (the London International Financial Futures and Op-tions Exchange)—offer trading of standardized weather contracts. CME offers futuresand options on futures based on indexes of HDDs and CDDs for selected populationcenters and energy hubs with significant weather-related risks throughout the UnitedStates as well as for some European cities.9 LIFFE trades only weather futures and thesefuture contracts are settled against monthly and winter season indexes bases on dailyaverage temperatures in a number of European cities.10

DEVELOPMENT OF WEATHER DERIVATIVES MARKET

The weather derivatives market traces its roots to the deregulation of the U.S. energyindustry. According to Climetrix, the weather team of RMS (Risk Management Solutions,Inc.), variability in weather conditions has always been recognized as one of the mostsignificant factors affecting energy consumption. However, the effects of unpredictableseasonal weather patterns were previously absorbed and managed within a regulated,monopoly-like environment. With deregulation, the various participants in the processof producing, marketing, and delivering energy to U.S. households and businesses areexposed to weather as a new and significant risk to their financial bottom line.11 Thebirth of the weather derivatives market can be traced to the trade based on the HeatingDegree Days (HDDs) in Milwaukee for the winter of 1997–1998, announced by KochIndustries and Enron.

Since 1997, the weather derivatives market has evolved into an active risk managementsector. According to the latest survey of the weather market, conducted jointly by Price-WaterhouseCoopers and the Weather Risk Management Association12 (Weather RiskManagement Association, Survey Report 2002), 8,758 weather contracts were transactedbetween October 1997 and March 2002. Altogether, these transactions represented ap-proximately $11.8 billion of notional exposure. The North American market was theindustry’s largest, with 7,189 contracts and a $10.9 billion notional value for that pe-riod. The European market recorded in all 969 contracts worth a total notional value of$721 million. In Asia, 562 contracts worth a total of $139 million were completed. The Aus-tralian market, although significantly younger and smaller than the others, accountedfor 21 contracts worth over $27 million. Temperature-based weather transactions werethe most prevalent. In the period of October 14, 1997 to April 15, 2001, temperature-related contracts represented over 98 percent of all weather contracts, while rain-relatedcontracts accounted for 0.9 percent, snow 0.5 percent, and wind 0.2 percent.13

9 For details see Weather Products, Chicago Mercantile Exchange, at http://www.cme.com/prd/wec.

10 For details see the London International Financial Futures and Options Exchange atwww.liffe.com.

11 See Climetrix, RMS, Inc., at http://www.climetrix.com.12 The Weather Risk Management Association (WRMA) was developed to serve the weather risk

management business by promoting the industry, providing forums for discussion and in-teracting with others associated with financial weather products. For more information, seehttp://www.wrma.org.

13 See the Weather Risk Management Association (http://www.wrma.com), Survey Report 2002.


The rapid growth of the weather derivatives market is attributed to the realization bycompanies that their businesses are no longer at the mercy of the weather now thatweather derivatives are available. The recognition and management of weather risks isspreading through the energy sector to electricity and natural gas utilities. Today, the bulkof the demand for weather risk management products still stems from the energy sector,but other industries, such as agriculture,14 insurance, tourism, and retail, are starting totake note (Sloan, Palmer, and Burrow, 2002). On the supply side of the weather derivativesmarket, various market participants offer weather risk management products. Energytrading firms, insurance companies, and the capital markets are all well represented inboth trading and origination activities of weather derivatives. Just like other derivativeswith exotic underlyings, weather derivatives have great potential to become a new assetclass for investors to diversify their portfolios.

BASIS RISK AND WEATHER HEDGING

Although most trading in the weather market is still over the counter, some standardizedweather derivatives are now listed on the CME and the LIFFE. Exchange-based weathertransactions have grown substantially since their introduction in 1999.15 Exchanged-based transactions provide price transparency and eliminate the counterparty defaultrisk through the promise of the clearing house. However, in trading in standardizedweather derivatives, hedgers must bear the basis risk, which is the risk due to the contractbeing written in a different location than the area the hedger wishes to cover. While theOTC weather market includes most U.S. cities, the exchange-based market includesonly around 15 cities.16 This means that participants wishing to manage their weatherexposures in cities not listed by exchanges face basis risk (Considine, 2000).

Basis risk is an important concern in hedging with standardized contracts. The fu-ture of standardized weather derivatives also depends on the magnitude of basis risk.Ederington (1979) shows that the degree of basis risk a firm faces in using a hedginginstrument can have a substantial effect on the usefulness of the instrument in reducingrisk. Haushalter (2000) finds that the likelihood of hedging by the oil and gas producersis related to the basis risk associated with hedging instruments. Other studies on basisrisk and the hedging effectiveness of traditional derivatives include Hill and Schneeweis(1982), Figlewski (1984), Chang and Shanker (1986), Moser and Helms (1990), Castelino(1992), Garcia (1996), Mahul (2002), and Miffre (2004). The basis risk of some derivativeswith exotic underlyings, such as insurance derivatives, has also been analyzed in theliterature (see, for example, D’Arcy and France, 1992; Harrington, Mann, and Niehaus,1995; Harrington and Niehaus, 1999; Major, 1999; Cummins, Lalonde, and Phillips, 2004).

Weather derivatives are a rather recent development, and research on the basis risk ofweather derivatives is relatively limited. Brockett, Wang, and Yang (2003a) analyze thebasis risk and hedging effectiveness of HDD/CDD-indexed weather derivatives in theU.S. electricity market. They conduct a historical analysis of hedging effectiveness for

14 In agricultural markets, crop insurance, derivatives on crop yields, and some revenue contractsare also available to manage quantity (or yield) risks for farmers.

15 See Weather Products, Chicago Mercantile Exchange, at http://www.cme/prd/wec.16 Only ten U.S. cities were listed on the CME before the recent addition of five further cities.


four U.S. Independent System Operators (ISOs)17—California (CAISO), the Electric Re-liability Council of Texas (ERCOT), Pennsylvania–New Jersey–Maryland (PJMISO), andNew York (NYISO)—and the eight climate regions within ERCOT. Two types of stan-dardized weather indexes are used—ten U.S. city indexes listed on CME,18 and ten U.S.regional indexes proposed by RMS (Risk Management Solutions, Inc.).19 Hedging effec-tiveness is compared between seasons and among months, between different underlyingindexes, and between diversified and undiversified power providers. In their analysis,the authors consider only a linear hedging strategy, that is, the hedging strategy usingweather futures and/or forwards to manage weather risks.

Based on their sample (four ISOs and eight subregions within ERCOT) and the linearhedging strategy, Brockett, Wang, and Yang conclude that undiversified firms shouldnot hedge the winter weather risk because of the significant basis risk. They also findthat February is the month with the greatest basis risk in the present weather derivativesmarket setting. In addition, their results suggest that CME and RMS indexes are almostidentical in terms of hedging effectiveness, and that neither provides an effective hedgingfor diversified power producers operating in CAISO or ERCOT. These findings enhanceto some extent our understanding of the present weather derivatives market and provideuseful suggestions for possible improvements.

Much work is needed to analyze the basis risk of weather derivatives to determine thesurvivability of current and proposed standardized weather contracts and to designmore effective standardized weather derivatives. A possible extension is to explore anation-wide analysis of the basis risk and hedging effectiveness of weather derivatives,and a further possible extension is to investigate the basis risk and hedging effectivenessfor individual companies. In addition, nonlinear hedging strategies as well as otherhedging objective functions are a number of other interesting topics to explore in futureresearch.

CREDIT RISK AND WEATHER HEDGING

Basis risk opens up the possibility of a market in the differential between exchange-quoted locations and locations not quoted on the exchanges. To perhaps reduce theproblem of basis risk, the hedger can use a number of “basis derivatives,” includingbasis swaps and basis options, to hedge basis risk (see, for example, MacMinn, 1999;Considine, 2000). Basis derivatives are written on the difference between two prices, twoindexes, etc. Weather derivatives are written on the difference of weather indexes at twodifferent locations. For example, a weather derivative might be written on the differencebetween CDDs in Birmingham and Atlanta in a given period of time (Considine, 2000).

17 An ISO is an independent, unbiased third-party entity that oversees the activities related to thereliable and safe transmission of electricity within a specific geographic area. Some ISOs haveestablished centralized markets for buying and selling energy in their respective regions.

18 The ten U.S. cities listed on CME are Atlanta, Chicago, Cincinnati, Dallas, Des Moines, Las Vegas,New York, Philadelphia, Portland, and Tucson.

19 RMS introduced ten regional weather indexes to provide the weather market with a new bench-mark for tracking and managing weather risk. These ten regions are: Mid-Atlantic, Midwest,Mountain States, Northeast, Northern Plains, Pacific Northwest, Plains, South Central, South-east, and Southwest.


Basis weather derivatives can be used to manage basis risk, but they also bring thehedgers some credit risk as basis weather derivatives are OTC contracts.

Credit risk, the risk of loss in the event that a counterparty to a transaction fails toperform a contractual obligation, exists in trading over the counter where the basisrisk is absent (Banks, 2002). Johnson and Stulz (1987) indicate that default is often apossibility that must be taken seriously. Many models have been developed to predictfinancial distress and bankruptcy (see, for example, Altman, 1968; Brockett et al., 1994;Altman and Saunders, 1997; Cummins, Grace, and Phillips, 1999; Carson and Hoyt,2000) and to price financial derivative contracts subject to credit risk (see, for example,Johnson and Stulz, 1987; Jarrow and Turnbull, 1995; Jarrow and Yu, 2001). In the literature,some studies analyze the optimal hedging strategies when the hedger faces nonperfor-mance or credit risk (see, for example, Hentschel and Smith, 1997; Cummins and Mahul,2003a), and other research investigates the demand for insurance by policyholders whopurchase insurance from credit-risky insurers (see, for example, Tapieo, Kahane, andJacque, 1986; Doherty and Schlesinger, 1990; Cummins and Mahul, 2003b). Credit riskhas attracted much attention in the weather market since Enron’s bankruptcy.20 Since thedemise of Enron, analysts are increasingly focused on the credit quality of energy tradingfirms, with several being downgraded, some to junk status (Sloan, Palmer, and Burrow,2002).

To address the trade-off between basis risk and credit risk in optimal weather hedg-ing, Brockett, Wang, and Yang (2003b) analyze the risk-sharing efficiency effects of ba-sis hedging, the joint use of exchange-traded weather derivatives and basis weatherderivatives to manage weather risks, with consideration of unhedgeable credit riskand hedgeable basis risk.21 Their study allows the hedger to use a weather derivativebased on a standardized weather index, which is correlated to its quantity demand.Basis risk exists when the correlation between the standardized weather index and thehedger’s quantity demand is less than 1. The hedger can use a separate weather deriva-tive (basis derivative) to cover the difference between the standardized weather indexand the hedger’s local weather index, which is assumed to have a higher correlationthan the standardized weather index, or a perfect correlation, with the hedger’s quantitydemand.

Brockett, Wang, and Yang analyze the basis-hedging problem for the U.S. power market.The weather indexes considered are HDDs and CDDs. In their hedging models, thepower producers under quantity risks (caused mainly by weather events) are assumedto maximize the mean-variance of their terminal wealth by using weather derivativesto manage their weather exposures. The authors also assume that there is no price risk,so the wealth-hedging problem is equal to the hedging quantity risk only. In addition,the weather risk market is assumed to be unbiased, that is, the premium of a weatherderivative is equal to the expected value of its payoff. In their models, firms can useboth linear hedging and nonlinear hedging strategies to hedge their weather exposures.

20 Before its demise, Enron was the largest dealer in the weather derivative market.21 For a similar analysis, see Doherty and Richter (2002). They analyze risk-sharing efficiency effects

due to the use of index-linked insurance derivatives and particularly the joint use of these toolsand indemnity insurance, with consideration of the impact of moral hazard.


Linear hedging is defined as selling weather forwards and/or futures (short positions),while nonlinear hedging is defined as buying weather put options (long positions), basedon different weather indexes.

The authors conduct a series of simulations to illustrate the determinants of hedge ratiosand hedging effectiveness. For the simulations, they assume that weather indexes aremultivariate normally distributed. Their simulation results indicate that linear and non-linear basis hedging are more effective when the correlation between the local weatherindex and the exchange-listed weather index is high and the standard deviation of the lo-cal weather index is large. Generally, they show that credit risk does not have significantimpact on linear basis hedging effectiveness when the standard deviation of the localweather index and the correlation between the local weather index and the exchange-listed weather index are not very low, whereas nonlinear basis hedging effectivenessincreases in credit risk unless the standard deviation of the local weather index is veryhigh.

Empirical analyses for a number of U.S. cities are also given in the study. Their em-pirical analysis uses two types of standardized weather indexes: ten CME city indexesand ten RMS regional indexes. Their sample includes 12 U.S. cities. A representativeweather station is selected for each of these 12 cities. Minimum, maximum, and averagedaily temperature from January 1, 1979 to April 30, 2002 are obtained from the NationalClimatic Data Center (NCDC) for these local weather stations. The credit risk levels con-sidered are 0.10, 0.05, and 0.01, which are the probabilities of issuer default. The weatherderivatives considered are seasonal contracts for hedging summer and winter seasons,and are assumed to be at money.

The authors’ empirical results indicate that RMS regional indexes are more effective thanCME city indexes for both summer and winter seasons, and for both linear and nonlinearbasis-hedging strategies. Most important, basis hedging using RMS regional indexes ismore effective compared to local hedging. The empirical results also indicate that linearbasis hedging is much more effective than nonlinear basis hedging as far as the riskminimization objective is concerned, and, generally, basis hedging is more effective forthe winter season than for the summer season.

VALUATION OF WEATHER DERIVATIVES

Since the inception of the weather derivatives market, the number and type of marketparticipants have continuously expanded. A variety of market participants offer weatherrisk management products, including integrated energy trading firms, insurance com-panies, hedge funds, and investment and commercial banks. Each market has its ownproduct line and pricing models (Sloan, Palmer, and Burrow, 2002). In practice, thesecontracts are commonly valued by the expected payoff under the physical measure,discounted at the risk-free rate, i.e., an actuarial approach (Davis, 2001).

Although actuarial valuation approaches have been very successful in the insurancemarkets, they are not appropriate for pricing weather derivatives (Sloan, Palmer, andBurrow, 2002). One striking feature of the actuarial valuation principles is that they areformulated within a framework that completely ignores the financial markets. However,weather events clearly affect the prices of some liquid assets in the financial market, and


weather derivatives can therefore be partially hedged by these liquid assets that arestochastically related to the payoff of weather derivatives (see, for example, Roll, 1984;Saunders, 1993; Craft, 1998; Kamstr, Kramer, and Levi, 2000; Hirshleifer and Shumway,2001).

As to financial valuation principles, the Black–Scholes method is the most successfulpricing approach in the area of derivatives. This method is based on a strategy in whichone creates a portfolio that accurately replicates the payoff of the derivative. The riskassociated with the financial derivative is thereby completely eliminated or hedged.Thus, one can argue that the value of a product must be the cost of setting up thehedging portfolio, based on the no-arbitrage principle. The Black–Scholes method hasbeen a landmark in derivative pricing in the complete market. A financial market iscomplete if all claims are attainable, i.e., if all claims can be replicated by means of aself-financing strategy. Despite its success, the Black–Scholes approach breaks down inthe incomplete markets (Young and Zariphopoulou, 2002).

If claims exist, which are not attainable, and hence cannot be replicated by means of anyself-financing trading strategies, then the market is incomplete. The weather derivativesmarket is an incomplete market model (Davis, 2001). The most distinctive feature ofweather derivatives is that, unlike traditional financial derivatives, their prices are linkedto a weather event rather than the price of an underlying security or commodity. Thecommonly used underlying weather indexes—for example, heating degree day (HDD),cooling degree day (CDD)—are nontradable. On the other hand, there is typically littleor no liquidity in weather derivatives (Davis, 2001). As such, the traditional no-arbitragepricing models of financial derivatives, such as the Black–Scholes model, cannot beapplied to price weather derivatives (see, for example, Dischel, 1998; Cao and Wei, 2000;Davis, 2001).

Various alternative pricing mechanisms have been developed for the incomplete mar-kets, including super-replication (El Karoui and Quenez, 1995), quadratic approaches(Follmer and Sondermann, 1986; Schweizer, 1988, 1991; Bouleau and Lamberton, 1989;Duffie and Richardson, 1991), quantile hedging and shortfall minimization (Cvitanic,1998; Follmer and Leukert, 1999, 2000), the marginal utility approach (Davis, 1998), andindifference pricing (Hodges and Neuberger, 1989; Davis, Panas, and Zariphopoulou,1993). Since incomplete financial market models acknowledge both the hedgeableand unhedgeable risks, they are more appropriate for the valuation of weatherderivatives.

Some researchers have attempted to explore the problem of weather derivative valuationin the incomplete market. Cao and Wei (2000) propose and implement an equilibriumvaluation framework for weather derivatives. They generalize the Lucas model of 1978to include weather as a fundamental variable in the economy. Their numerical analysesshow that the market price of risk associated with the temperature variable is insignificantin most cases, especially when risk aversion is high or when the aggregate dividendprocess is close to a random walk. Their results also show that the so-called historicalsimulation method can lead to significant pricing errors due to its erroneous implicitassumptions. Davis (2001) explores weather derivative pricing using the marginal utilityapproach, based on the assumption that agents in the weather derivatives market are notrepresentative but face very specific weather risks. In his article, accumulated HDDs and


commodity prices are modeled as geometric Brownian motions, which lead to explicitexpressions for swap rates and option values.

Brockett, Wang, and Yang (2003c) adopt an incomplete market pricing model—the in-difference valuation approach—to analyze the valuation of weather derivatives. Theindifference valuation approach stems from the economic principle of certainty equiv-alent,22 but is modified and extended to accommodate partial hedging in the financialmarket. In a mean–variance framework, the relationship between weather derivatives’indifference prices and the transaction volume is examined, and a number of conditionsare obtained when the actuarial price is not an appropriate valuation for weather deriva-tives. By comparing the buyers’ and sellers’ indifference prices, the authors also examinethe conditions for the viability of the weather derivatives market. In addition, by examin-ing explicitly the distributional impacts of all the stochastic variables involved, Brockett,Wang, and Yang investigate the impacts of partial hedging, natural hedges, basis risk,quantity risk, and price risk on the investors’ indifference prices.

In practice, most issuers of weather contracts write a large portfolio to take advantageof geographic diversification and hedging effects. For hedgers, they would desire touse a combination of standardized weather contracts and basis weather derivativesdesigned to hedge the basis risk of the standardized contracts. Single contracts shouldthen be priced in the context of the marginal changes they cause to the portfolio ratherthan on their stand-alone performance (Jewson et al., 2002). Also in a mean–varianceframework, Brockett et al. (2003) adopt the indifference pricing approach to examinethe portfolio effects on weather derivatives’ indifference prices. In their article, portfolioeffects are defined as the effects on the indifference prices of weather derivatives wheninvestors usually hold a portfolio of weather derivatives and other financial assets. Theirsimulation results illustrate how the magnitude of the portfolio effects is related to thecorrelation between weather indexes, between weather indexes and the payoff of therisky assets in the financial market, and to some other distributional characteristics of therelevant stochastic variables, as well as to the payoff structures of the weather contractsalready in the investor’s portfolio.

CONCLUSION

Weather derivatives constitute a comparatively recent type of financial product devel-oped to hedge weather risks, and currently represent the fastest-growing derivativemarket. This article presents an overview of weather risks, weather derivatives, and theweather derivatives market, and examines the valuation issue of weather derivatives inthe incomplete market, the hedging effectiveness of standardized weather derivatives,as well as optimal weather hedging with consideration of basis risk and credit risk.

When trading in standardized weather contracts, hedgers must bear the basis risk, andat the same time they must bear credit risk when trading over-the-counter. Basis risk,credit risk, and hedging effectiveness are important issues and deserve greater attentionin future research. In addition, since neither actuarial valuation approaches nor completemarket pricing models are appropriate to value weather derivatives, further work isneeded to develop a consistent and widely acceptable valuation model to foster thegrowth of the weather derivatives market. Now that both price derivatives and weather

22 See Gerber and Pafumi (1998) for a detailed overview of the principle of equivalent utility.


derivatives are available for hedgers, another interesting topic for future research is todetermine the role of weather derivatives in corporate dual hedging with both price andvolume/quantity risks.

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Weather Derivatives and Weather Risk Management

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