05/01/02Goldman Sachs: Energy Derivatives et al Copyright (C) 2002, Marshall, Tucker & Associates,...

05/01/02 Goldman Sachs: Energy Derivatives et al Copyright (C) 2002, Marshall, Tucker & Associates, LLC. All rights reserved.

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Goldman, Sachs & CompanyControllers UniversityCapital Markets Group

Module 4, Session 6

Credit, Weather, Energy, Insurance& Precious Metal Derivatives

Alan L. Tucker, Ph.D.631-331-8024 (tel)631-331-8044 (fax)

[email protected]

Copyright © 2002Marshall, Tucker & Associates, LLC

All rights reserved


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ALAN L. TUCKER, Ph.D.

Alan L. Tucker is Associate Professor of Finance at the Lubin School of Business, Pace University, New York, NY and an Adjunct Professor at the Stern School of Business of New York University, where he teaches graduate courses in derivative instruments and fixed income analytics. Dr. Tucker is also a principal of Marshall, Tucker & Associates, LLC, a financial engineering and derivatives consulting firm headquartered in New York. Dr. Tucker was the founding editor of the Journal of Financial Engineering, published by the International Association of Financial Engineers (IAFE). He presently serves on the editorial board of Journal of Derivatives, Financial Decisions, Derivatives Risk Management Service, and the Global Finance Journal and is a former associate editor of the Journal of Economics and Business. He is a former director of the Southern Finance Association and a former program co-director of the 1996 and 1997 Conferences on Computational Intelligence in Financial Engineering, co-sponsored by the IAFE and the Neural Networks Council of the IEEE.

Dr. Tucker is the author of three books on financial products and markets: Financial Futures, Options & Swaps, International Financial Markets, and Contemporary Portfolio Theory and Risk Management (all published by West Publishing, a unit of International Thompson). He has also published more than fifty articles in academic journals and practitioner-oriented periodicals including the Journal of Finance, the Journal of Financial and Quantitative Analysis, the Review of Economics and Statistics, the Journal of Banking and Finance, Virginia Tax Review, and many others.

Dr. Tucker has contributed to the development of the theory of derivative products including futures, options and swaps, and to the theory of international capital markets and trade. He has also contributed to the theory of technology adoption over the life-cycle. The Social Sciences Citation Index shows that his research has been cited in refereed journals on over one hundred occasions.

As a consultant, Dr. Tucker has worked for The United States Treasury Department, the United States Justice Department, Morgan Stanley Dean Witter, Union Bank of Switzerland-Paine Webber, Goldman Sachs, Deutsche Bank, LG Securities (Korea), and Chase Manhattan Bank. Dr. Tucker holds the B.A. in economics from LaSalle University (1982), and the MBA (1984) and Ph.D. (1986) in finance from Florida State University. He was born in Philadelphia in 1960, is married (Wendy) and has three children (Emily, 1993, Michael and Matthew, both 1995).


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Energy Derivatives et al

Purpose:

The purpose of this seminar is to present the basics of particular derivative products and their applications. The products addressed are credit, weather, energy, insurance, and precious metal derivatives. Thereafter we emphasize the complexity of valuing these products by focusing on a particular pricing application, namely the pricing of American-style crack spread options.

The products described herein are principally traded over the counter, although there are a handful of exchange-listed products that witness some limited trading volume. Examples include weather futures and futures options at the Chicago Mercantile Exchange and of course oil futures contracts traded on the New York Mercantile Exchange and the International Petroleum Exchange.


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Credit Derivatives:

A credit derivative is a contract where the payoff depends on the credit worthiness of one or more commercial or sovereign entities. Its purpose is to allow credit risks to be traded and managed in much the same way as market risks like interest rate risk or foreign exchange rate risk.

The principal types of credit derivatives are:

(1) Credit Default Swaps

(2) Total Return Swaps

(3) Credit Spread Options



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(1) Credit Default Swap (CDS)

A CDS provides insurance against the risk of a default by a particular entity. The entity is known as the “reference entity” and a default by said entity is known as a “credit event”. The buyer of the insurance obtains the right to sell a particular bond issued by the entity for its par value when a credit event occurs. The bond is known as the “reference obligation” and the total par value of the bond that can be sold is known as the swap’s “notional principal”.

The buyer of the CDS makes periodic payments to the seller until the end of the life of the CDS or until a credit event occurs. A credit event, such as a missed coupon payment on the bond, usually requires a final accrual payment by the buyer. The swap is then settled either by physical delivery or in cash. If in cash, the determination agent



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polls bond dealers to determine the mid-market price, B, of the reference obligation some specified number of days after the credit event. The cash settlement is then (100 - B)% of the notional principal.

Example. A five-year CDS, $100MM NP, buyer agrees to pay 90 bps annually ($900,000). A credit event occurs in, say, 3.5 years. Under physical settlement, the CDS buyer turns over the reference obligation to the CDS seller in return for $100MM. Under cash settlement, if the determination agent finds that the post-credit event mid-market price, B, is $35 per $100 of par, the cash payoff would be $65MM. In either case, the CDS buyer must pay the seller the amount of the annual payment accrued since the last payment - here approximately $450,000.



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There are a number of variants of the basic CDS including:

Binary CDS: The payoff in the event of a default is a specific dollar amount and is therefore independent of the bond’s post-event value.

Basket CDS: A group of reference entities is specified, and there is a payoff when the first of these defaults (known as

a “first to default clause”).

Contingent The payoff requires both a credit event and an additional CDS: trigger, such as a specified movement in a

related market variable.

Dynamic CDS: The notional amount determining the payoff is linked to the marked-to-market value of a portfolio of swaps.



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(2) Total Return Swap (TRS)

In a TRS, the return from one asset or group of assets is swapped for the return on another. The TRS is mostly used to pass credit risks on to another party or to diversify credit risk by swapping one type of exposure for another.

Example. Consider a farm bank in Tennessee that has an asset portfolio consisting mainly of loans to tobacco farmers. There is a concentration of credit risk related to the tobacco industry including litigation against the tobacco companies. This farm bank could swap the total return on its tobacco loan portfolio in return for the total return on another portfolio that is more diversified across industrial and geographical lines.



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(3) Credit Spread Option (CSO)

A CSO is an option on the spread between the yields earned on two assets. The option provides a payoff whenever the spread exceeds some level (the strike spread).

Example. An investor holds dollar-denominated bonds issued by a sovereign foreign government, say Russia. The investor could purchase a CSO that pays off whenever the yield on the bond exceeds the yield on a comparable-maturity US Treasury by 800 basis points. The payoff would be calculated as the difference between the value of the Russian bond with a 800 basis point spread and the market value of the bond. The CSO thereby limits the investor’s exposure to the underlying sovereign credit.



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Weather Derivatives:

The US Department of Energy estimates that 14% of the US economy is subject to weather risk. So it is not surprising that weather derivatives were introduced beginning in 1997.

Most weather derivatives depend on two measured variables: (1) HDD (heating degree days), and (2) CDD (cooling degree days):

(1) HDD = max(0, 65 - A) (2) CDD = max(0, A - 65)

where A is the average of the highest and lowest temperature during the day (midnight to midnight) at a specified weather station, in Fahrenheit. For example, if the high and low for a day were 68 degrees and 44 degrees, then A = 56 and HDD = 9 and CDD = 0.



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Typical weather derivatives are forward and option contracts providing a payoff dependent on the cumulative HDD or CDD during a calendar period.

Example. A dealer sells PECO Energy a call on the cumulative HDD during November 2001 at the Philadelphia International Airport weather station with a strike of 700 and a payment rate of $10,000 per degree day. If the actual cumulative HDD is 820, the payoff is $1.2MM.

Weather derivatives often have a payment cap, say $1MM in the previous example. Here the contract is equivalent to a bull money spread as the client is long a call on cumulative HDD with a strike of 700 and short a call with a strike of 800.



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By far, the most common users of weather derivatives are energy companies as HDD and CDD are proxies for the volume of energy required for heating and cooling respectively. Other users include agricultural companies, firms in the leisure industry (e.g., ski lift operators), and the like.

The Chicago Mercantile Exchange introduced weather futures and futures options in September 1999 for 10 different weather stations: Atlanta, Chicago, Cincinnati, Dallas, Des Moines, Las Vegas, New York, Philadelphia, Portland, and Tucson.

Weather derivatives are priced using historical temperature data which are used to provide a probability distribution of the product’s payoff. The mean of the payoff distribution is discounted at the risk free rate because weather has no systematic risk. Temperature trends and seasonal factors are accommodated.



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• www.cme.com (Chicago Mercantile Exchange)

• www.wrma.org (Weather Risk Management Association)



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Energy Derivatives:

Unlike credit and weather derivatives, many energy products trade both OTC and on exchanges. We examine here trading in derivatives on three energy products:

(1) Crude Oil

(2) Natural Gas

(3) Electricity



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(1) Crude Oil Derivatives

About 65 million barrels (8.9 million tonnes) of crude oil is consumed daily worldwide. Ten-year fixed-price supply contracts have been commonplace in the OTC market for many years. These represent swaps where oil at a fixed price is exchanged for oil at a floating price. OTC forward and option contracts on crude oil are also popular. Settlement can be in cash or in physical delivery.

Exchange-traded futures and futures options on crude oil also exist, and can also have cash or physical settlement. For example, Brent crude oil futures on the IPE are cash settled whereas light sweet crude oil futures on the NYMEX require physical delivery.

The NYMEX also trades derivatives on refined oil products including heating oil and gasoline and on “crack spreads”.



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Hedging Example: It is October 25, 2001 and a company knows that it will need to purchase 20,000 barrels of crude oil at some time in February or March of 2002. Oil futures contracts are currently traded for delivery every month on NYMEX, and the contract size is 1,000 barrels. The company therefore decides to use the April 2002 contract for hedging and takes a long position in 20 April 2002 contracts. The futures price on October 25 is $18.00 per barrel. The company finds that it is ready to purchase the crude oil on March 10, 2002. It therefore closes out its futures contract on that date via a reversing trade. The spot price and futures price on March 10, 2002 are $20.00 per barrel and $19.10 per barrel, respectively.

The gain on the futures contract is $19.10 - $18.00 = $1.10 per barrel. The basis when the contract is closed out is $20.00 - $19.10 = $0.90 per barrel. The effective price paid (in dollars per barrel) is the final spot price less the gain on the futures or $20.00 - $1.10 = $18.90. This can also be calculated as the initial futures price plus the final basis or $18.00 + $0.90 = $18.90. The total price paid is $18.80 x 20,000 = $378,000.



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(2) Natural Gas Derivatives

The natural gas industry has been going through a period of deregulation and the elimination of state monopolies. Suppliers, who are faced with the task of meeting daily demand, are not necessarily the producer.

A typical OTC contract is for the delivery of a specified amount of natural gas at a roughly uniform rate over a one-month period. Forward contracts, options, and swaps are available OTC. The seller of gas is usually responsible for moving the gas through pipelines to the specified location. NYMEX trades a contract for the delivery of 10,000 million BTUs of natural gas requiring physical delivery to a hub in Louisiana. The IPE trades a similar contract in London.



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(3) Electricity Derivatives

Electricity is very difficult to store. Thus there is a maximum supply of electricity in a region at any given moment that is determined by maximum capacity of all electricity producing plants in said region at that moment. In the US there are 140 regions known as “control areas”. Demand and supply are first matched within a control area and any excess power is sold to other control areas. It is this excess power that constitutes the wholesale market for electricity.

The ability of one control area to sell to any other depends on the transmission capacity of the lines between the two areas. Transmission involves a cost charged by the owner of the line(s) and there are generally some transmission or energy losses.



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Given non-storability, finite capacity in a region, and frictions associated with transmitting electricity from region to region, there can be occasional price spikes in regional electricity costs at the wholesale level, particularly during summer months. Heat waves have increased the spot price of electricity by as much as 1000% for short periods of time. The per annum vol of electricity is commonly 100% to 200% whereas it is only about 20% for crude oil and 40% for natural gas. All three commodities exhibit mean reversion and seasonal price swings.

Like natural gas, electricity has been going through a period of deregulation and the elimination of state monopolies. This has been accompanied by the development of an electricity derivatives marketplace. NYMEX now trades a futures contract on the price of electricity and there is an OTC market in forwards, options and swaps.



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A typical contract (exchange traded or OTC) allows one side to receive a specified number of megawatt hours for a specified price at a specified location during a particular month. In a 5 x 8 contract, for example, power is received for 5 days a week (Monday-Friday) during the 8-hour off-peak period (11 p.m.-7 a.m.) for the specified month. In a 5 x 16, power is received 5 days a week for the 16 peak hours.

Option contracts have either daily exercise or monthly exercise. With the former, the option holder can choose on each day of the month (by giving one day’s notice) to receive the specified amount of power at the specified strike price. With the latter, a single decision is made at the beginning of the month to receive power for the whole month at the strike price.



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In both the electricity and natural gas markets, another popular product is a “swing option”, which is also known as a “take-and-pay option”. Here a minimum and maximum for the amount of power that must be purchased at a certain price by the option holder is specified for each day during a month and for the month in total. The option holder can change (“swing”) the rate at which the power is purchased during the month, but usually there is a limit on the total number of swings that can be made.

Hedging Energy Risk. An energy producer faces two forms of risk, price risk and volume risk. Although prices adjust to reflect volumes, there is a less-than-perfect relationship between the two, and energy producers have to take both into account when developing a hedging strategy. The price risk can be hedged using energy derivatives; volume risk is hedged by using weather derivatives.



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Let Y be monthly profit, P the average energy price for the month, and T the relevant temperature variable (HDD or CDD) for the month.

An energy producer can use historical data to obtain a best fit linear regression relationship of the form

Y = a + bP + cT + e

where e is an error term. The energy producer can then hedge risks for the month by taking a position of -b in energy forwards or futures and a position of -c in weather forward or futures. The relationship can also be used to analyze the effectiveness of alternative option strategies.



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• www.nymex.com



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Insurance Derivatives:

Many insurance companies have subsidiaries that trade derivatives and many of the activities of insurance companies are becoming very similar to those of investment banks.

Traditionally, insurance companies have hedged their exposure to catastrophic (CAT) risks such as hurricanes and earthquakes in a process known as “reinsurance”. Reinsurance contracts take a number of forms. An example is an “excess-of-loss” contract that covers “excess cost layers”. Here the first level of CAT loss recovered from reinsurance kicks in at say $30MM (an “attachment point”) and ends at $40MM (a “detachment point”). The second layer might apply from $40-$50MM, and so on. Clearly each layer’s reinsurer has written a bull spread on the total losses. Lump-sum/binary reinsurance contracts are also popular.



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Reinsurance is provided by reinsurance companies and “Lloyds syndicates”, which are unlimited liability syndicates of wealthy individuals.

Hurricane Andrew in 1992 caused about $15 billion of insurance losses in Florida, exceeding the total relevant premiums received from Florida property and casualty insurers for the previous seven years combined. This triggered increases in insurance and reinsurance premiums and a search for more ways to diversify insured risk.

The most popular of these alternatives has been the CAT bond. This is a bond issued by a subsidiary of an insurance company that pays a higher-than-normal interest rate. In return, the holder of the bond agrees to provide an excess-of-cost reinsurance contract. Principal or interest or both can be used to satisfy claims depending on the terms of the CAT bond. These bonds can add diversification to most institutional portfolios as catastrophic risk is presumably unsystematic.



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Precious Metal Derivatives:

There is a vast derivatives marketplace worldwide - both exchange-traded and OTC - for precious metals including copper, gold, platinum, silver, palladium, and titanium.

Precious metals are classified as “investment assets” as opposed to “consumption assets” such as oil, electricity and natural gas. [This is because precious metals are storable and tend to be traded for speculative or investment reasons (even though they have other uses, e.g., silver in pharmaceuticals), whereas consumption assets tend to be difficult to store and are generally traded for consumption only.] This is an important distinction for valuation purposes as arbitrage arguments can be used to obtain exact solutions for the prices of derivatives traded on investment assets, whereas arbitrage arguments can only provide upper bounds on the prices of derivatives written on consumption assets.



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Precious metals do not throw off income (like dividends on a stock or coupons on a bond). Precious metals also present storage costs including insuring the asset. Storage costs can be regarded as negative income.

If U is the present value value of all the storage costs that will be incurred on a holding of a precious metal during the life of futures contract, it follows from arbitrage arguments that

F(0) = [S(0) + U]exp(rT),

where F(0) is the current precious metal futures price, S(0) is the precious metal cash price, r is a continuously-compounded risk free interest rate with maturity T years - the same maturity as the futures contract.



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If the storage costs incurred at any time are proportional to the price of the precious metal, they can be regarded as providing a negative dividend yield and we have:

F(0) = [S(0)]exp(r + u)(T)

where u is the storage costs p.a. expressed as a proportion of the cash price.

For example, consider a one-year futures contract on gold. Suppose that it costs $2 per ounce per year to store gold, with payment being made at the end of the year. Assume that the cash price is $270 and the one-year risk free rate is 5%, so S(0) = $270, r = .05, T = 1, U = $2 x exp(-.05 x 1) = $1.9025, and

F(0) = ($270 + $1.9025) x exp(.05 x 1) = $285.84.

If the quoted futures price was, say, $300, an arbitrageur would buy gold, store it, and short the one-year futures contract to profit (and vice-versa).



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As another example of pricing precious metal derivatives, consider an exchange-traded American-style call option on a gold futures contract. Let the futures mature in six months and the futures option in 3 months. Let the current six-month futures price be $270 per ounce and let the strike on the call be $265 per ounce. Let the three-month risk free rate be 4% with continuous compounding, and let the volatility of gold be 11% per annum. Then the call futures option price (mid-market) is obtained from a straightforward application of the binomial option pricing model and is $8.6147 per ounce or $861.47 per contract. (See software demonstration with 30-step tree.)



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Complex Pricing:

Unfortunately, ascribing a price to some of the derivatives presented here today is much more difficult than the examples just illustrated for gold futures and futures options contracts.

Consider, for instance, an American-style crack spread option traded on the NYMEX. This is an option product that allows for early exercise and that is a function of two state variables - one refined and one unrefined (e.g. heating oil and crude oil) - thus implying a three-dimensional pricing problem (the two state variables, which of course are in some way correlated, and time).

The attached article describes a technique for pricing such an option.

(See “Bivariate Binomial Options Pricing with Generalized Interest Rate Processes,” by Hilliard, Schwartz and Tucker, Journal of Financial Research (1996), 585-602.)



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• www.riskcenter.com



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Suggested Readings:

Arditti, Cai and Cao, “Whether to Hedge,” RISK Supplement on Weather Risk (1999), 9-12.

Canter, Cole and Sandor, “Insurance Derivatives: A New Asset Class for the Capital Markets and a New Hedging Tool for the Insurance Industry,” Journal of Applied Corporate Finance (1997), 69-83.

Clewlow, and Strickland, “Energy Derivatives: Pricing and Risk Measurement,” Lacima Group, 2000.

Das, Credit Derivatives: Trading & Management of Credit & Default Risk,” Singapore: John Wiley and Sons, 1998.

Eydeland, and Geman, “Pricing Power Derivatives,” RISK (October 1998), 71-73.



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Geman, “CAT Calls,” RISK (September 1994), 86-89.

Hanley, “A Catastrophe Too Far,” RISK Supplement on Insurance (July 1998).

Hull, “Fundamentals of Futures and Options Markets,” Englewood Cliffs, NJ: Prentice Hall, 4th edition, 2002.

Hull, and White, “Valuing Credit Default Swaps I: No Counterparty Default Risk,” Journal of Derivatives (2000), 29-40.

Hunter, “Managing Mother Nature,” Derivatives Strategy (1999).

Joskow, “Electricity Sectors in Transition,” The Energy Journal (1998), 25-52.

Kendall, “Crude Oil: Price Shocking,” RISK Supplement on Commodity Risk (1999)



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Litzenberger, Beaglehole, and Reynolds, “Assessing Catastrophe Reinsurance-Linked Securities as a New Asset Class,” Journal of Portfolio Management (1996), 76-86.

Nikkah, “How End Users can Hedge Fuel Costs in Energy Markets,” Futures (1987), 66-67.

Tavakoli, “Credit Derivatives: A Guide to Instruments and Applications,” New York: John Wiley and Sons, 1998.



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