© 2007 Thomson Delmar Learning, a part of the Thomson Corporation Chapter 6 Fundamentals of Options Hedging

© 2007 Thomson Delmar Learning, a part of the Thomson Corporation

Chapter 6Chapter 6

Fundamentals of Fundamentals of Options HedgingOptions Hedging


OptionsOptions

The goal of this chapter is to provide an The goal of this chapter is to provide an introduction to options, one of the most introduction to options, one of the most powerful risk management tools.powerful risk management tools.

An option when bought is the right but not the An option when bought is the right but not the obligation to either buy or sell something in obligation to either buy or sell something in the future. the future.

An option is a double derivative, being based An option is a double derivative, being based on the underlying futures market, which in on the underlying futures market, which in turn is based on the cash market.turn is based on the cash market.


Option BasicsOption Basics

The buyer of an option is buying the right, but The buyer of an option is buying the right, but not the obligation, to buy (not the obligation, to buy (callcall) or sell () or sell (putput) ) something at some point in the future.something at some point in the future.

The seller of an option has an obligation to The seller of an option has an obligation to perform if the buyer perform if the buyer exercisesexercises the option. the option.

If the buyer If the buyer lets thelets the option expireoption expire,, the seller’s the seller’s obligation is dissolved.obligation is dissolved.

(continued)(continued)


Option Basics Option Basics (continued)(continued)

The seller’s compensation for taking on the The seller’s compensation for taking on the responsibility is called the responsibility is called the premiumpremium..

The price, if exercised, is called the The price, if exercised, is called the strike strike priceprice..

Options are strong contracts and can be Options are strong contracts and can be retraded.retraded.

The initial buyer has three choices: exercise, The initial buyer has three choices: exercise, let expire, or retrade by selling.let expire, or retrade by selling.


The Insurance ConceptThe Insurance Concept

The owner of an insurance policy has purchased the The owner of an insurance policy has purchased the right but not the obligation to use the benefits; the right but not the obligation to use the benefits; the underwriter has agreed to the obligations of the underwriter has agreed to the obligations of the coverage.coverage.

For this reason, options are often referred to as price For this reason, options are often referred to as price insurance.insurance.

Options on futures are traded or offered on the Options on futures are traded or offered on the exchanges at various strike prices at fixed intervals exchanges at various strike prices at fixed intervals above and below the futures price with corresponding above and below the futures price with corresponding premiums. (See Figure 6-1, next slide.)premiums. (See Figure 6-1, next slide.)



Options: Strike PriceOptions: Strike Price

At the moneyAt the money means that the strike price is the same means that the strike price is the same as the underlying futures price.as the underlying futures price.

In the moneyIn the money means that for puts (calls), the strike means that for puts (calls), the strike prices are above (below) the at-the-money price.prices are above (below) the at-the-money price.

Out of the moneyOut of the money means that the strike prices for means that the strike prices for puts (calls) are below (above) the at-the-money strike puts (calls) are below (above) the at-the-money strike price.price.

At-the-money strike price is composed only of At-the-money strike price is composed only of time time valuevalue..


OptionsOptions

The length of time to expiration of the option is The length of time to expiration of the option is directly related to the time value.directly related to the time value.

The time value for options is the probability of a price The time value for options is the probability of a price move.move.

Option premiums also have Option premiums also have intrinsic valueintrinsic value..– All in-the-money options have positive intrinsic value.All in-the-money options have positive intrinsic value.– All out-of-the-money options have negative intrinsic value.All out-of-the-money options have negative intrinsic value.

Only positive intrinsic values are counted.Only positive intrinsic values are counted. Positive intrinsic value is merely a bookkeeping concept.Positive intrinsic value is merely a bookkeeping concept.

When assessing the time value of options, the When assessing the time value of options, the variability of prices and length of time to maturity are variability of prices and length of time to maturity are critical.critical.


Options Pricing: The PremiumOptions Pricing: The Premium

The premium is simply the price at which the The premium is simply the price at which the options contract trades.options contract trades.

That price is determined by supply and demand.That price is determined by supply and demand. Other than buyers and sellers, a third party existsOther than buyers and sellers, a third party exists

—arbitragers keep markets honest and liquid.—arbitragers keep markets honest and liquid. The Risk and Mitigation Profile process is the The Risk and Mitigation Profile process is the

best approach for hedgers to determine whether best approach for hedgers to determine whether any particular options contract meets their needs.any particular options contract meets their needs.


Black-Scholes Options Pricing ModelBlack-Scholes Options Pricing Model

The BSOPM was developed for European The BSOPM was developed for European options on stocks, not commodity futures.options on stocks, not commodity futures.

Figure 6-3 describes the model (see slide).Figure 6-3 describes the model (see slide). Pit traders and arbitragers know how the Pit traders and arbitragers know how the

model reacts to a change in any of the model reacts to a change in any of the variables.variables.



Black-Scholes Options Pricing Model Black-Scholes Options Pricing Model (continued)(continued)

The BSOPM is dependent upon several assumptions:The BSOPM is dependent upon several assumptions:– All relevant markets are efficient.All relevant markets are efficient.

– Interest rates are constant and known.Interest rates are constant and known.

– Returns are lognormally distributed random variables.Returns are lognormally distributed random variables.

– No commissions are paid.No commissions are paid.

– The option can only be exercised on expiration.The option can only be exercised on expiration. The last assumption forces the model to specifically The last assumption forces the model to specifically

address European options.address European options.(continued)(continued)


Black-Scholes Options Pricing Model Black-Scholes Options Pricing Model (continued)(continued)

The BSOPM yields a theoretical premium. The BSOPM yields a theoretical premium. Market imperfections or differences between reality Market imperfections or differences between reality

and assumption cause disparity between premiums. and assumption cause disparity between premiums. Relevant differences are:Relevant differences are:– The true underlying distribution of prices is not exactly The true underlying distribution of prices is not exactly

lognormally distributed.lognormally distributed.– Borrowing and lending rates are different.Borrowing and lending rates are different.– Volatility expectations differ among market participants.Volatility expectations differ among market participants.– The market is less liquid than it usually is or is The market is less liquid than it usually is or is

theoretically expected to be.theoretically expected to be. BSOPM remains the cornerstone of premium BSOPM remains the cornerstone of premium

determinations.determinations.


Option Pricing: The Greek ValuesOption Pricing: The Greek Values

The BSOPM is based on several major The BSOPM is based on several major variables.variables.

These variables are explained in Figure 6-3These variables are explained in Figure 6-3(see next slide).(see next slide).



Buying Puts and CallsBuying Puts and Calls Buyers of options have at least seven different strike price/ Buyers of options have at least seven different strike price/

premium combinations to choose from.premium combinations to choose from. Option buying truncates the loss of trading at the premium Option buying truncates the loss of trading at the premium

level.level. (See Table 6-1, next slide.) (See Table 6-1, next slide.) Buyers have unlimited gain potential with loss limited to the Buyers have unlimited gain potential with loss limited to the

premium.premium. Sellers have limited gain potential with unlimited loss Sellers have limited gain potential with unlimited loss

potential.potential. Buyers of call options are speculating that the price of the Buyers of call options are speculating that the price of the

underlying futures contract will increase.underlying futures contract will increase. Buyers of put options are speculating that the price of the Buyers of put options are speculating that the price of the

underlying futures contract will decrease.underlying futures contract will decrease.



Writing Puts and CallsWriting Puts and Calls

To To writewrite an option is to accept the responsibility of an option is to accept the responsibility of performing in case the buyer decides to exercise the performing in case the buyer decides to exercise the option.option.

Option writing truncates the gains of trading at the Option writing truncates the gains of trading at the premium level.premium level.

Writers of options can write the option either Writers of options can write the option either coveredcovered or or nakednaked..– A covered writer will have the underlying futures contract A covered writer will have the underlying futures contract

the option is written against.the option is written against.– A naked writer does not have the underlying futures and is A naked writer does not have the underlying futures and is

promising to provide one in case the buyer exercises the promising to provide one in case the buyer exercises the option.option.


Writing PutsWriting Puts If a writer has a naked put, the writer will gain the If a writer has a naked put, the writer will gain the

premium if the price of the underlying futures premium if the price of the underlying futures increases.increases.

Table 6-3 shows the results of a price increase and Table 6-3 shows the results of a price increase and decrease on a naked put.decrease on a naked put.– Writers of naked puts are bullish.Writers of naked puts are bullish.

Table 6-4 shows the results of a put that is covered. Table 6-4 shows the results of a put that is covered. The effects are the opposite of a naked put. The effects are the opposite of a naked put. – Writers of covered puts are bearish.Writers of covered puts are bearish.

Put option writers will cover the option if they are Put option writers will cover the option if they are bearish and leave the option naked if they are bullish.bearish and leave the option naked if they are bullish.– Figures 6-8 and 6-9 illustrate these concepts.Figures 6-8 and 6-9 illustrate these concepts.


Writing CallsWriting Calls

A call writer who is bullish will write the call A call writer who is bullish will write the call covered. This writer earns the maximum covered. This writer earns the maximum possible when prices increases.possible when prices increases.– Writer earns only the premium.Writer earns only the premium.

A call writer who is bearish will leave the A call writer who is bearish will leave the option naked.option naked.– Writer earns the premium if prices fall.Writer earns the premium if prices fall.

Figures 6-10 and 6-11 illustrate these concepts.Figures 6-10 and 6-11 illustrate these concepts.


Writing versus Buying OptionsWriting versus Buying Options

A bullish option writer can either write a call A bullish option writer can either write a call covered or write a put naked.covered or write a put naked.– These have the same returns. They are These have the same returns. They are

mechanically different, but alike financially.mechanically different, but alike financially.– Likewise bearish writers can write a call naked or Likewise bearish writers can write a call naked or

write a put covered.write a put covered. Writing options covered or naked is simply Writing options covered or naked is simply

done to reverse the direction of price done to reverse the direction of price expectation and not done for any risk expectation and not done for any risk management reasons.management reasons.



Writing versus Buying OptionsWriting versus Buying Options (continued)(continued)

The problem with writing options is risk The problem with writing options is risk management.management.– Losses are potentially unlimited.Losses are potentially unlimited.– Written options have limited value as a hedging Written options have limited value as a hedging

tool.tool. Buying options is a valid risk management Buying options is a valid risk management

tool because losses are limited and gains are tool because losses are limited and gains are unlimited.unlimited.– The concept of counterbalance holds.The concept of counterbalance holds.


Option HedgingOption Hedging

Because gains are limited with written options, Because gains are limited with written options, buying options will be used in simple hedging.buying options will be used in simple hedging.

Hedging with options creates the right but not Hedging with options creates the right but not the obligation to hedge with a futures contract.the obligation to hedge with a futures contract.



Option Hedging Option Hedging (continued)(continued)

Put Option HedgingPut Option Hedging– A corn producer could hedge his crop against A corn producer could hedge his crop against

falling prices by selling a corn futures contract, he falling prices by selling a corn futures contract, he could also do this by buying a put option on corn could also do this by buying a put option on corn futures. If prices dropped, he could exercise the futures. If prices dropped, he could exercise the option and have a futures hedge; if prices go up, he option and have a futures hedge; if prices go up, he can let it expire.can let it expire.

– Table 6-7 shows these actions.Table 6-7 shows these actions. Call Option HedgingCall Option Hedging

– A feed company that has forward sold feed could A feed company that has forward sold feed could use options to hedge as shown in Table 6-8.use options to hedge as shown in Table 6-8.


Floors and Ceilings with Floors and Ceilings with Option HedgingOption Hedging

Tables 6-7 and 6-8 and Figures 6-12 and 6-13 Tables 6-7 and 6-8 and Figures 6-12 and 6-13 illustrate the concept of price floors and ceilings.illustrate the concept of price floors and ceilings.

With a put option hedge in Figure 6-12, the price With a put option hedge in Figure 6-12, the price floor the producer will receive is $2.35 per bushel.floor the producer will receive is $2.35 per bushel.

In Figure 6-13, the price ceiling the feed company In Figure 6-13, the price ceiling the feed company will receive is $2.65 per bushel.will receive is $2.65 per bushel.

Hedging with futures provides a price floor, but at Hedging with futures provides a price floor, but at the same time provides a price ceiling.the same time provides a price ceiling.


Hedging to a Certain Price/CostHedging to a Certain Price/Cost

This can be done because options have several This can be done because options have several strike prices to pick from when hedging.strike prices to pick from when hedging.

Put option hedgers can subtract the premium Put option hedgers can subtract the premium from the strike price and derive the price floor, from the strike price and derive the price floor, known as the known as the target pricetarget price..

Call option hedgers concerned about a price Call option hedgers concerned about a price ceiling can find a ceiling can find a target costtarget cost, which is the call , which is the call strike price less the premium.strike price less the premium.– This is illustrated by Tables 6-9 and 6-10.This is illustrated by Tables 6-9 and 6-10.


Target Price HedgingTarget Price Hedging

A cattle producer can calculate his target price A cattle producer can calculate his target price and have this valuable information before he and have this valuable information before he has to make a decision. The rancher could buy has to make a decision. The rancher could buy an out-of-the-money put option at $96 to have an out-of-the-money put option at $96 to have a target price of $95.55/cwt. The rancher’s a target price of $95.55/cwt. The rancher’s gross profit will be $0.55/cwt as shown in gross profit will be $0.55/cwt as shown in Table 6-11.Table 6-11.

The target price hedge becomes the price floor.The target price hedge becomes the price floor. Higher guaranteed profits come at a price.Higher guaranteed profits come at a price.


Target Cost HedgingTarget Cost Hedging

Table 6-10 shows costs of feeder cattle relative to the Table 6-10 shows costs of feeder cattle relative to the initial strike price used as a hedge. A cattle feeder initial strike price used as a hedge. A cattle feeder could use this to calculate her target cost. If she could use this to calculate her target cost. If she determines she can pay no more than $98/cwt, she determines she can pay no more than $98/cwt, she could buy a call at the $97 strike price. The target could buy a call at the $97 strike price. The target cost will be $97.50/cwt.cost will be $97.50/cwt.

The cattle feeder would achieve her strike price and The cattle feeder would achieve her strike price and reduce costs $.40/cwt.reduce costs $.40/cwt.

This is a management decision that can be made prior This is a management decision that can be made prior to the production decision using target cost hedging.to the production decision using target cost hedging.


Partial Coverage HedgingPartial Coverage Hedging

Sometimes only a certain level of protection is Sometimes only a certain level of protection is desired. This could be due to the cost of full desired. This could be due to the cost of full coverage or the hedger is speculating that coverage or the hedger is speculating that prices will move in her favor.prices will move in her favor.

This would lead the buyer to purchase an This would lead the buyer to purchase an option at a strike price that is farther out-of-the option at a strike price that is farther out-of-the money. money.

Table 6-13 illustrates this.Table 6-13 illustrates this.


Option Multiple HedgingOption Multiple Hedging

The relationship between the value of the option and The relationship between the value of the option and the underlying futures price is called delta.the underlying futures price is called delta.– Delta = change in the option premium/change in futures price.Delta = change in the option premium/change in futures price.– Deltas range from zero to one.Deltas range from zero to one.

Deltas impact the concept of counterbalance.Deltas impact the concept of counterbalance.– For every dollar of futures change, the option premium For every dollar of futures change, the option premium

only changes $0.50 with a delta of 0.5.only changes $0.50 with a delta of 0.5.– See Table 6-14.See Table 6-14.

To achieve a dollar equivalency between futures and To achieve a dollar equivalency between futures and options hedges requires a options hedges requires a multiplemultiple..– multiple = 1/deltamultiple = 1/delta



Option Multiple Hedging Option Multiple Hedging (continued)(continued)

Central idea behind deltas and multiples is to Central idea behind deltas and multiples is to understand how the value of the option as a hedge understand how the value of the option as a hedge changes as the futures price changes.changes as the futures price changes.

Hedgers that desire to have a dollar value equivalency Hedgers that desire to have a dollar value equivalency throughout the hedging period need to throughout the hedging period need to scale the scale the hedgehedge..– See Tables 6-15 and 6-16.See Tables 6-15 and 6-16.

The process of scaling option hedges attempts to The process of scaling option hedges attempts to achieve achieve delta neutral hedgesdelta neutral hedges. A true delta neutral . A true delta neutral hedge would achieve perfect dollar equivalency.hedge would achieve perfect dollar equivalency.


Final Word on DeltasFinal Word on Deltas

Deltas of necessity have to be calculated after Deltas of necessity have to be calculated after the fact. Thus they are always historic and the fact. Thus they are always historic and static.static.

Markets constantly change, resulting in hedges Markets constantly change, resulting in hedges constantly needing to be scaled, thus constantly needing to be scaled, thus increasing the cost.increasing the cost.

A wise option hedger is aware of the A wise option hedger is aware of the importance of deltas and their limitations.importance of deltas and their limitations.


Synthetic Futures HedgeSynthetic Futures Hedge

Option buying combined with option writing can Option buying combined with option writing can mimic a futures hedge. (See Table 6-17.)mimic a futures hedge. (See Table 6-17.)

The synthetic set of options has the exact same result.The synthetic set of options has the exact same result. This type of hedge is favored by some brokers This type of hedge is favored by some brokers

because the client has to pay two commissions for the because the client has to pay two commissions for the options versus one for a futures hedge.options versus one for a futures hedge.

This type of hedge also parrots a futures hedge and This type of hedge also parrots a futures hedge and costs more to place. It should be avoided.costs more to place. It should be avoided.

One popular type of a synthetic hedge involves One popular type of a synthetic hedge involves buying out-of-the-money and selling in-the-money, buying out-of-the-money and selling in-the-money, earning an initial cash flow for the hedger. (See Table earning an initial cash flow for the hedger. (See Table 6-18.)6-18.)


Options Hedge versus Futures HedgeOptions Hedge versus Futures Hedge

Options are a superior way to hedge sometimes and Options are a superior way to hedge sometimes and inferior at other times.inferior at other times.

Options are referred to as Options are referred to as “second best”“second best” because an because an option hedge is less effective than an futures hedge option hedge is less effective than an futures hedge when prices move against your cash position.when prices move against your cash position.

““Second best” can only be judged after the fact.Second best” can only be judged after the fact. If prices are forecasted to move against the cash If prices are forecasted to move against the cash

position, hedge with futures. If prices are forecasted position, hedge with futures. If prices are forecasted to move in favor of the cash position, hedge with to move in favor of the cash position, hedge with options.options.

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© 2007 Thomson Delmar Learning, a part of the Thomson Corporation Chapter 6 Fundamentals of Options Hedging