Research " Financial Derivatives in Corporate Risk Management " potx

MacMinn This dissertation addresses how the weather derivative hedges the corporate risk, how to price the indexed derivative as an exotic derivative instrument, and the implications of

The Dissertation Committee for Mulong Wang Certifies that this is the approved version of the following dissertation:

Financial Derivatives in Corporate Risk Management

Committee:

Patrick L Brockett Supervisor’s name, Supervisor

Richard D MacMinn Co-Supervisor’s name, Co-Supervisor

Jonathan F Bard Member’s name

Douglas J Morrice Member’s name Thomas W Sager Member’s name

Financial Derivatives in Corporate Risk Management

by Mulong Wang, B.S

Dissertation

Presented to the Faculty of the Graduate School of

the University of Texas at Austin

in Partial Fulfillment

of the Requirements for the Degree of

Doctor of Philosophy

The University of Texas at Austin

August 2001

UMI Number: 3036610

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Dedicated to Helen,

My wife

I also would like to thank my dear wife, Helen With her consistent encouragements and help, I can dedicate to this research

Drs Jonathan Bard, Douglas Morrice and Thomas Sager provided numerous comments on this dissertation Their service on

my dissertation committee is greatly appreciated

Colleagues in Center of Risk Management and Insurance and Center of Management and Operations for Logistics also provided a lot

of help in my PhD student career Their discussions inspired a lot of this dissertation research and other research projects

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Financial Derivatives in Corporate Risk Management

Publication No

Mulong Wang, Ph.D

The University of Texas at Austin, 2001

Supervisors: Patrick L Brockett and Richard D MacMinn

This dissertation addresses how the weather derivative hedges the corporate risk, how to price the indexed derivative as an exotic derivative instrument, and the implications of basis risk embedded in the weather derivative

The traditional one-dimension financial market framework is expanded to include the weather index Under this expanded framework, the stock market values of the unhedged and hedged firms are studied first This provides the base to investigate the pricing formula for weather derivative under the expanded framework

It is found that both financial and actuarial approaches are integrated

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to price the weather derivative

A positive risk management paradigm must provide the criteria

to choose the optimal hedging instrument(s) for separable risks This dissertation provides the criteria to choose optimal hedging contract set to hedge the weather risk, under different corporate leverage levels It has been found that weather derivative outperforms the traditional commodity forward in most of the scenarios When corporate leverage levels increase, the positive role of the weather derivative or the commodity forward diminishes

Basis risk arises by introducing the standard weather index, and providing the industry-standard payment when the weather derivative is exercised The implication of basis risk is investigated under the same expanded framework It is found that in most of the scenarios, basis risk is innocuous

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TABLE OF CONTENTS

Chapter I Introduction………1

1.1 Background……….2

1.2 Literature on Risk and Risk Management………….7

1.3 The Frontier of Risk Management ……….11

1.4 Weather Risk and Weather Derivatives ………13

Chapter II Weather Derivative and Its Valuation……….17

2.1 Introduction………17

2.2 Basic Model ………28

2.3 Valuation of Weather Derivative……… 38

Chapter III Weather Derivative and Commodity Forward…… 48

3.1 Scenario sets………49

3.2 Optimal Hedging…… ……….58

Chapter IV Basis Risk and Its Implications……….86

4.1 Introduction……….86

4.2 Implications of Basis Risk………89

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Appendix I Figures ………106 Appendix II Extensions of Principle of Increasing Uncertainty…125

Reference……….135 Vita………142

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Chapter I

Introduction

This dissertation addresses how the weather derivative hedges the corporate risk, how to price the indexed derivative as an exotic derivative instrument, and the implications of basis risk These topics are summarized in an expanded uncertainty model Under this framework, different hedging instruments for studying the optimal hedging portfolios are compared

In economics and finance literature, risk has been a subject of interest and study in many fields including management science, decision science, and psychology With the new risks being continuously discovered, innovative strategies and tools were created

to manage them or transfer them In this chapter, the background of risk creation, identification and the importance of risk management are discussed first In the second chapter, the economic and financial literature on risk and risk management, most of which concentrates

on the mechanism of financial derivatives to hedge the risk, or insurance contract to transfer the individual risk or corporate risk, is reviewed The third chapter studies the new frontier of risk management strategies and tools In the last part, the weather

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derivative is introduced as an example of novel risk management tool The focus of this dissertation is to study how the weather derivative hedges the specific risk and its positive effects on creating value for the hedged firms The valuation of the indexed derivative was investigated and the comparison of different hedging instruments in the corporate finance framework was made, to investigate the optimal hedging strategies under the presence of separable risks

This dissertation investigated the pricing problem of the weather derivative In addition, the comparison of the weather derivative and the commodity forward under different corporate leverage scenarios was made Finally, the implications of basis risk were discussed

1.1 Background

In general, risk is the uncertainty in the future, and has been traditionally separated into two categories: pure risk or speculative risk A pure risk is a chance of loss or no loss, and a speculative risk

is characterized as a chance of loss or gain An example of pure risk is catastrophe risk, such as an earthquake, flood or hurricane Gambling is an example of speculative risk, which may yield a gain or

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loss in the end

In the economics and finance literature, the definitions of pure risk and speculative risk differentiate insurance from finance Much of the insurance literature has concentrated on the management of pure risk and much of the finance literature on risk management has concentrated on the management of speculative risk However, recent applications of risk management have blurred the line between these fields For example, the Catastrophe (CAT) Bond, created to hedge the catastrophic event risk, is an example of securitization, seen mostly in the mortgage market However, the separation between insurance and finance paradigms was blurred by the creation of the CAT bond Like investing in traditional bonds, i.e., Treasury bonds or corporate bonds, investors bear the speculative risk The cedent, paying the premium to the safe trust, obtains the protection as traditional insurance provides Therefore, CAT bond is not only an investment vehicle for the investors, but also a hedging vehicle for the cedents, which represents a vehicle combining both pure risk and speculative risk With the discovery of new risks, new hedging instruments will be developed to further blur the line of pure risk and speculative risk, making the distinction between insurance and finance even more

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ambiguous

Nowadays, the risk-management process is becoming an increasingly important financial area for virtually all corporations With the dramatically growing costs of losses from different risk sources, business firms can gain a competitive cost advantage through the development of a set of cost-effective and efficient risk-management strategies The advantages of a well-managed risk management program include not only a lower total loss cost and an improved business bottom line, but also an increased predictability of future losses and cost, which ensures greater budget control and reduced ambiguity for future net revenue stream A less risky corporate operation and payoff preserve more value for the risk-averse investors and therefore are preferred In addition, a good risk management program will immunize the corporation from the sharp loss in the lower tail of the loss distribution curve [c.f Stulz (1996)] Another advantage for an efficient risk management program may be

a lower cost of employment, since workers are more willing to be employed in a financially stable firm with a lower wage than work in a risky firm In summary, an efficient risk management program will not only reduce the level of losses incurred by a firm, but it will also

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help the firm improve its financial performance and employee morale

From a corporate finance perspective, risk management is becoming a more important field For instance, during 1990, U.S domestic firms spent more than $6001 billion on projects related to risk management, such as product liability, workers’ compensation, employee health, dental, disability and pension benefits, and other insurance- related products Research has disclosed that firms typically pay approximately 40% of their payroll costs on risk management activities with health care and employee benefits alone, which account to approximately 26% of the cash flow of a typical firm For instance, General Motors Corp spent more than $4 billion on health care costs for its employees and is now attempting to cut the costs by transferring some of it to employees Recently, large jury verdicts awarding compensations to customers or employees of business have skyrocketed, making risk management even more important for businesses These types of costs of uncontrolled risk can, and have, bankrupted corporations while clearly focusing other corporations on the importance of managing and controlling their own

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1 See George Rejad’s Principle of Risk Management and Insurance

risks

An integral part of managing risk is to transfer the financial impacts of such risks to another party, if possible, or if the transfer is not too expensive Historically, a common mechanism for such transfers is to use the insurance industry to retain these transferred risks, by assuming the insurance companies are risk neutral Theoretically, the law of large numbers, which states that as the number of independent and identically distributed risks becomes arbitrarily large, the standard deviation of the average loss distribution converges toward zero, makes the insurance industry viable and profitable In fact, apart from government regulation, insurance may still be the single most important mechanism for regulating risk and safety in society, though many alternative risk-transferring vehicles have been introduced and implemented recently Risk management and insurance costs and protection are also important for individual consumers Individuals traditionally purchase automobile, homeowners, and other insurance to stabilize their financial conditions, and prepare for uncontrollable risks such

as accidents, death or illness

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1.2 Literature on Risk and Risk Management

In the economics and finance literature, risk and risk management have drawn considerable attention One of the major instruments to manage risk is insurance At the corporate level, the role and impact of using insurance to transfer risk have been studied extensively [c.f MacMinn (1987a); Mayers and Smith (1987); MacMinn (1989); Garven and MacMinn (1993), MacMinn (1999)] Insurance is

an efficient instrument to manage the pure risk [c.f MacMinn (1999)], and preserves corporate value when there is a probability of insolvency At the individual level, the demand for insurance in an investor’s optimal portfolio was also investigated [c.f Doherty (1981); Doherty (1984); Doherty and Schlesinger (1983a); Doherty and Schlesinger (1983b); Mayers and Smith (1982); Mayers and Smith (1983)] In general, insurance has been demonstrated to be an indispensable risk-management instrument It was found that insurance should be included in the optimal investment portfolio when pure risk is present

The role that insurance plays in financial markets can be explained by distinguishing between risks The finance paradigm

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characterizes risk as systematic or non-systematic, or equivalently, diversifiable or non-diversifiable The insurance paradigm, however, classifies risks as either pure or speculative The different definition of risk separated finance from insurance literatures For a long time, finance and insurance were separated because of this line, and the convergence of hedging by financial instruments and insurance contracts was largely ignored

The main purpose of risk management is to preserve or create values by selecting optimal contract sets For firms, corporate value is preserved by the inclusion of hedging instruments in the financial contracts For individual investors, more expected utility is created by the inclusion of insurance and/or other hedging contracts in the investment portfolio Before the demise of the Glass-Steagall Act in the 1990s, insurance and finance industries were treated separately Recent mergers, particularly the merger between Citicorp and Travelers, represent the convergence of finance and insurance in practice These new acts and mergers changed the conditions and more risk management instruments are combined with insurance and financial techniques

It is not hard to follow the convergence trend The main

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function of financial markets is to efficiently allocate the risk and facilitate the redistribution of risk The development of financial markets has been benefited from the better understanding of separable risks When the risk becomes more transparent, it facilitates the redistribution process in the financial market Insurance contract is a subset of financial contracts If the combination of insurance and financial hedging contracts creates more value for the firm, it is preferred The recent convergence in the finance and insurance industries enhances the main function of risk management, that is, by efficiently combining risk management techniques, more value is created The development of catastrophe bond is a good example of the convergence of financial and insurance techniques By tapping the pure catastrophic risk into the financial market, a better allocation of risk and resource is achieved between firms and investors Consequently, more value is generated

Therefore, there is a need to extend the current economics and finance paradigms to better understand how the financial instruments can hedge the risk and allow an efficient allocation of risk bearing and resources Based on the extended paradigms, further studies on how to combine the different hedging instruments to reach

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the optimal allocation of risks and resources can then be made

A robust model to incorporate and compare different hedging instruments has not yet been developed in the literature A better understanding of risks and risk comparisons is needed, though a perspective for comparing risks has been provided [c.f., Rothschild and Stiglitz (1970)] The process of risk being generated and valued must also be well understood to compare different hedging instruments The optimal hedging contract set can then be chosen to preserve the most value

The recent developments of risk management instruments and financial markets reveal the continued separation of risks so that each can be redistributed at the least cost to society To understand this behavior, more fundamental notions and understanding of risks are required A robust model is needed to allow the risks to be valued separately and so the choices for an optimal hedging contract set can

be made

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1.3 The Frontier of Risk Management

With the convergence of finance and insurance, many new risk management tools were developed Alternative Risk Transfer (ART) is one subset of them With the rapid identification and separation of new risks, many of the ART solutions are tailored to specific client problems and offer integrated risk management solutions, for instance, a multi-year or multi-trigger cover ART solutions focus on increasing the efficiency of the risk transfer, broadening the coverage

of insurable risks and tapping the capital markets for additional capacity These risk management solutions make it easier for a company to efficiently manage those risks from which it gains no comparative advantage in managing itself The development of ART is consistent with the objective of an efficient risk- management solution

by allowing institutional clients to allocate more capital to their core businesses, thereby generating higher returns

Over the last few years, ART solutions have expanded rapidly The initial focus is on captives Such solutions will allow companies to deal with high-frequency risks in a more cost-efficient way than through traditional industrial insurance Since 1980s, captives have been increasingly used as a financing instrument for some low-

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frequent, but high-severity risks which could not be placed in the traditional ways Despite the continuous erosion of tax benefits and the persistently low premium rates in the traditional market during the 1990s, captives are set to come into their own as holistic risk management tools

The potential for the sustained growth of new risk management strategies and tools is considerable Captive is one example Other new instruments have been created and implemented Attempts to transfer insurable risks directly to capital market investors have received special attention over the past a few years This can be through the securitization of risks in the form of insurance bonds or via derivative transactions In this way, the policyholder obtains additional capacity without incurring any credit risk, in particular, for the catastrophe losses, while investors are able to further diversify their investment portfolios with the invention of new instruments such as CAT bonds

The rapid development of risk management instruments must

be based on a widely acceptable economic and/or financial mechanism for the instruments to efficiently hedge the risks For instance, weather derivatives may be a good example to hedge the

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weather-related risks To tap the capacity of financial markets, a widely understandable pricing formula and the positive role of adding weather derivative into the optimal contract set of the firm must be investigated In addition, the advantages and disadvantages of using those new hedging instruments must also be understood for them to

be widely implemented and traded

1.4 Weather Risk and Weather Derivatives

As different as they may be, the business and production processes of utility companies, theme parks, fashion houses, ice-cream manufacturers, building companies and sports goods manufacturers, all have one thing in common: their business success

is highly dependent on prevailing weather conditions Nearly everyone talks about the weather but few do anything about it Virtually all sectors of the economy are directly or indirectly subject to the influence of the weather in some form or other For instance, daily beer consumption can be increased if the temperature rises Weather risks are important to the energy and power supply industry because their product price is highly sensitive to the spot weather conditions The agriculture industry is another example Production level is highly

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correlated with weather conditions, which affects profit

Unusual weather patterns have increasingly prompted companies whose results are affected by the prevailing weather conditions to seek protections against effects of this kind An unusually warm winter may cut the revenue figure of a natural gas company, but an unusually cold winter may sharply increase the demand of natural gas

Hedging weather risks not only will yield a more predictable revenue stream, but also increase the shareholder’s value The energy and power sectors may benefit most from the new tools to hedge weather-related risks, with other hedging instruments including weather derivatives in the firm’s portfolio will stabilize the net revenue stream and reduce the loss of revenue in the lower tail of the weather-risk distribution

A weather derivative is an exotic derivative because the underlying asset is not negotiable or traded It is based on the weather index, such as Cool Degree Days or Heating Degree Days, which influence the volume of the goods, particularly the energy products, traded in the market Therefore, the major effect of weather derivatives is to hedge the volume risk, instead of the price risk For

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instance, a warmer-than-average winter season may drive the natural gas demand lower, thus a weather put2 option will be in the money and will provide compensations to the option buyer, since the weather index (HDD in this case) is below the strike value

The notion behind a weather hedge is that the results of weather-sensitive sectors can be subject to great volatility, even if prices remain unchanged, due to a change in demand or volume

An important, but unresolved issue is a unanimous pricing formula for the weather derivative This prevents the weather derivative from being traded efficiently in the market The underlying asset is not traded and the traditional Black-Sholes model cannot be applied In addition, the assumption of the log-normal distribution of the weather index, such as CDD or HDD, is difficult to verify due to the lack of a robust empirical test and consideration of seasonal change To solve this issue, the dynamism of the weather (trends) and the actuarial weather forecast information must be included in the pricing model to best reflect the value of weather derivatives

In general, risk is a commodity that may be produced, exchanged or preserved The way in which businesses and society

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2 A put option will be in the money when the index is below the strike value In the

assess, control and transfer risk has been examined extensively and with the invention of new risk management tools being studied continuously This dissertation is an attempt to examine how weather derivatives are incorporated into the corporate contract sets, how to price the indexed derivatives, and the implications of the basis risk The Appendix is an expansion of the uncertainty model [c.f., MacMinn and Holtmann (1983)], including more stochastic inputs, to examine whether the widely cited Principle of Increasing Uncertainty (PIU) may still hold in this extended model Chapter two discusses the inclusion

of the weather derivative into the firm’s hedging contract set and valuation of the weather derivative Chapter three delineates several scenarios based on corporate-leverage levels For each scenario, the impacts of different hedging strategies on the corporate value are studied In chapter four, implications for the corporate payoff and corporate value are studied when the basis risk is present

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warmer winter, the HDD index will be lower, since less heating is needed

Chapter II

Weather Derivatives and Its Valuation

2.1 Introduction

2.1.1 Weather Risk and The Creation of Weather Derivatives

In recent years, several unique conditions, e.g., unpredictable

weather conditions that affect corporate revenue, combined with the

need to manage risks produced one of the novel financial products of

the last decade: weather derivative The historical circumstances that

accelerated the development of the trading market include: unusual

weather conditions in different regions, and change of the demand for

weather-associated commodities, causing possible price risks These

extreme weather patterns exposed the high level of weather-related

risk embedded in the operations of many companies that, as a result,

affected both their revenues and net earnings For example, an

unusually cool summer will decrease the demand for ice cream or

electricity consumption because of the lesser use of air conditioning,

and an unusually cold winter will increase the demand for natural gas

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for heating purpose as in the past winter of 2000 In fact, virtually every sector of the economy is affected by the weather to one extent or another

Energy products may be the most sensitive to unusual weather conditions Weather remains the single largest variable in the energy spot-market price According to research by Koch Industrial and Utility Services [c.f., Richter (1998)], a 10 percent colder-than-normal temperature in summer can decrease the natural gas spot price by 15 percent If average heating-season temperatures rise 1.43 degrees Fahrenheit above normal, the drop in demand for natural gas will outweigh the increase in demand that occurs naturally each year to satisfy economic growth, forcing prices down overall Meanwhile, electric utilities also exhibit heightened weather sensitivity in the summer, and hydroelectric utilities are affected not only by temperature anomalies, but also by snow and rain anomalies Recent data for the unit price of natural gas over the past few years3 clearly shows a strong negative correlation between the temperature and the

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3 These data were kindly provided by Enron Capital

spot price for natural gas in Henry Hub4 (see Figure A in Appendix II)

To measure the correlation between weather conditions and earnings, it is necessary to have a generally acceptable way to interpret the weather conditions in different seasons, particularly the summer and winter In general, weather conditions are interpreted by the introduction of a weather index in different seasons A widely accepted weather index is Cooling-Degree-Days (CDD) in the summer

or Heating-Degree-Days (HDD) in the winter The daily HDD may be defined as the maximum of zero and the difference between 65 degrees Fahrenheit and the daily average temperature, where the daily average temperature is the average of the maximum and minimum temperatures (midrange) recorded at a designated reporting station during a 24-hour period beginning at midnight That is, if we let the daily average temperature be Ti, the daily number of “heating degrees” is HDDi =max(65 T ,0)− i and the accumulated “heating-

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4 Henry Hub is one of the major marketplace that Enron Capital uses to trace the energy commodity price in different seasons It provides research data to illustrate

degree-days” (HDD) over one month (30 days) period ending at date t

at date t is t 30 t i 1

i 1

X CDD− +

=

an overall low CDD numerical value

With broad applicability ranging from electric utilities to underwear companies to theme parks, the weather-derivative market has the potential to exceed the $200-billion electricity market, according to Enron Capital & Trade Inc The growing weather derivative market may help control its effects on businesses Through October 2000, there are more than a dozen companies actively engaged in the transactions of weather derivatives, making market capitalization about $2 billion6 The weather derivative is designed to manage the weather risk, a risk that does not have an immediate and

long-20

the relationship between energy commodity price and temperature

5 Therefore, the accumulated HDD by day 5 will be the sum of

HDD ,HDD , ,HDD

6 Provided by Swiss Reinsurance Co

direct impact on other risks It is usually written on an index of the weather conditions, such as CDDs or HDDs, and can take the form of calls, puts, swaps, caps, collars, or floors The weather-derivative market is in many ways a perfect area for the development of risk-management products The need for protection is universal and the information about weather conditions is widely available By efficiently targeting volumetric risk in situations in which price-based derivatives have previously fallen short, weather derivatives provide the ability to combine hedges on weather-related risks, such as temperature or precipitation, with a more typical price-based hedge

on energy commodities, such as natural gas or electricity tied to a weather index

A simple interpretation of weather options is provided in the following table:

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1996 in New York City’s Central Park In this contract, the embedded risk was that in a cooler-than-normal month spot-market prices for power would be lower than the fixed price at which Consolidated Edison Co had purchased the commodity In addition, a cooler summer will cut the electric sales for its Megawatt Store, causing revenue shortfalls By giving it a rebate for a cooler-than-normal

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summer, Consolidated Edison Co had the opportunity to recoup the lost opportunities in the spot market The detailed option structure was: if accumulated CDDs in August 1996 were from 0 to 10% below the expected 320 as weather stations did, the company received no discount to the power price, but if the accumulated CDDs were 11 to 20% below normal (320 in this case), Consolidated Edison Co received a $16,000 discount in total From 20 to 30% below normal, the discount value will be increased to $32,000, and if the total CDDs are more than 30% below 320, the maximum discount in total was

$48,000 In fact, August did have some muggy and cooler days, which reduced the total CDDs and provided protections for Consolidated Edison Co., which was what it wanted

One of the major obstacles to the universal acceptance of weather derivatives is that its valuation stays unresolved This is because the underlying “asset” (weather index as HDD or CDD) is untradeable This untradeable index separates the weather derivative from other traditional hedging instrument, because there is no basis

to price it as a financial derivative The underlying “asset” of the weather derivative is based on data such as temperature, which influences the trading volume of other goods Usually the weather

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index, i.e., the underlying “asset” in the weather derivative, can be interpreted as CDD, i.e., cooling-degree-days, or HDD, heating-degree-days This challenging valuation problem must be resolved to tap the weather derivative to the greater financial market Two competing paradigms exist: one is based on the application of actuarial techniques, and the other is based on the Black-Sholes approach to the pricing of derivatives The unique valuation challenges of weather derivatives may lead to the emergence of a hybrid approach and a new theory of valuation

A weather hedge is important because it can stabilize the forecast for the future revenue, or income stream, for the weather-sensitive sectors, thus a well-predictable business can result in increased shareholder value7 The objective of risk management is to preserve or create values for the firm If the revenue of the firm is sensitive to the weather conditions, for instance, an energy firm, hedging with weather derivatives will recoup part or all the revenue loss due to negative weather conditions When there is a risky leverage, the insolvency probability may be reduced or eliminated by

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7 As illustrated by the following sections, a hedged firm generally will have less risky production than unhedged one By taking a less risky position, corporate value is increased

hedging with weather derivatives Therefore, the bond value is preserved, and more corporate value is achieved For individual investors, investing in the energy firms hedged with weather derivative reduces the overall risk in the portfolio Assume that the investors are risk-averse, a portfolio with the same expected return but less risk will be preferred, since more expected utility is achieved, i.e., more value is created for the investors

The development of weather derivatives also represents one of the recent trends toward the convergence of insurance and finance [c.f., MacMinn (2000)] By efficiently tapping capital markets, this convergence will transfer the risk to a much larger capital capacity pool The creation of weather derivatives also challenges another fundamental difference in the way that insurance and financial industries solve the problem of risk management In general, the property/casualty insurance industry uses the principle of diversification, pooling many uncorrelated risks and charging a premium based on actuarial probabilities of occurrence of different risks and their correlations Financial derivatives in risk management are based on the option pricing and hedging algorithms, which were originally developed in the 1970s Which paradigm(s) should be

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selected to price the weather derivatives still remains unclear This paper is an attempt to price it in an expanded economic model, by integrating both the actuarial and financial approaches

2.1.2 Literatures on Economics and Finance

One of the fundamental research topics on the weather derivative is how to price this new hedging instrument Although the structure of the weather derivative and the mechanism of how it hedges the weather risk have been extensively studied [c.f., Leggio and Lien (2000), Muller and Grandi (2000), Richter (1998)], little research has been done to provide an explicit explanation of how to price the weather derivative In addition, most of the literature does not present

a model where the weather-related risk was incorporated into a robust economic framework, as an explicit source of uncertainty Economic and finance literature on the theory of the firm has concentrated on the uncertainty arising either from the demand of its product or from the firm’s technology [c.f., Leland (1972), MacMinn and Holtmann (1983)] In these studies, firms had a single source of risk: a one-dimension uncertainty framework None of the models had included

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multiple sources of risk In fact, one unique characteristic of weather risk is its independence with most other risks Consequently, it may

be considered as a second source of risk, in addition to other existing risk in the corporate finance literature

Another implication of using the weather derivative is from the basis risk Though basis risk has been extensively interpreted recently [c.f., MacMinn (2000)], few studies quantified basis risk according to the corporate finance perspective It is widely known that the basis risk arises from using a standard industry index By using the standard index, some of the problems often hampering risk management, such as moral hazard and adverse selection, are eliminated Basis risk may also arise when a standard index is used Some of the most recent empirical work on corporate hedging behavior [c.f., Haushalter (2000)] revealed that firms would prefer to use hedging instruments with little basis risk An explicit explanation

in a theoretical framework has not yet been provided and the implications of basis risk for corporate hedging remains unclear

An economic model to explicitly incorporate weather risk into the firm’s payoff structure was presented in this chapter Several important questions arising from using the weather derivatives were

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addressed For example, how to quantify the weather risk in an incomplete financial market; whether the incorporation of weather derivatives in the firm’s contract set adds value; whether the role of weather derivatives can be duplicated by other hedging instruments such as swaps or forwards, and if so, an alternative pricing formula may be provided for the weather derivative based on the no arbitrage principle; what is the optimal contract set to hedge the weather; what are the positive and negative impacts by using different set of hedging instruments? Chapter four discusses further whether the basis risk should be hedged or retained under different conditions

be resolved at time t 1= All financial and operation decisions are made now while all payoffs on those decisions will be received then In the standard complete financial market model, an economic state may

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be interpreted as an index of economic conditions and it is assumed that there are as many stock contracts, i.e., the basis stock, as there are states of nature, and each basis stock contract pays one dollar in

a particular state and zero otherwise A corporate stock may then be interpreted as a portfolio of these basis stock contracts It follows that

in a complete financial market, a corporate stock is a speculative risk

The economy is composed of individual investors, who make their investment portfolios to maximize the utility, and corporations where there are managers, who make operation and financial decisions on behalf of the shareholders One simple interpretation of the managers’ objective is to maximize the current shareholders’ market value With the inclusion of weather risk, the otherwise complete financial market becomes incomplete In the economy constructed with weather risk, the state space is expanded and the weather index z is incorporated For simplicity, throughout this wdissertation, the weather index is assumed as heating-degree-days (HDD), and a natural gas utility firm is the object firm being studied Therefore, “then” defined in this model may be interpreted as a winter season

With the inclusion of the weather index into the original model,

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the state space is interpreted now as (z , z ) Ze w ∈ e ×Z The variable w z e

is interpreted as an index of economic conditions and Ze =[0, ] is the ωset of these index numbers The variable z represents a weather wstate and Zw =[0, ]υ 8 is the set of these states Throughout this dissertation, the weather index z represents different HDDs in the wwinter season The weather risk is a speculative risk, i.e., weather-related loss could be positive or negative If it is positive, it means the natural gas utility suffers a loss because of the weather condition, i.e., the HDDs are below the neutral level If it is negative, it means the firm gains from the weather conditions, i.e., the HDDs are above the neutral level

The corporate net payoff is represented as Π(q,z , z )e w , including the impacts from economic and weather conditions The firm’s payoff function is Π =P(z , z )q c(q), where e w − P is the unit price of the firm’s product then, and c(q) is the cost function for a production level of q

If the cost function is assumed convex, the corporate payoff is concave

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8 This is the set of HDD values for the observation period Based on the definition of HDD in the first part (Introduction) of this chapter, the sum of the daily HDD number over the observation period must be at least zero

in production level It is a competitive firm facing with price uncertainty The firm’s payoff function is satisfied with the principle of increasing uncertainty (see Appendix)

w

Z represents higher HDDs at time t 1= Let o = 0

Z {z } be the neutral weather state, i.e., the actual HDDs coincide with the forecast

of weather stations Table 2 presents the components of this model

z Strike value selected by firm

Π Firm’s payoff function

q Firm’s production level

For the firm studied in this dissertation, a HDD put option is

31