© 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 Options The goal of this chapter is to provide an introduction to options, one of the most powerful risk management tools. The goal of this chapter is to provide an introduction to options, one of the most powerful risk management tools. An option when bought is the right but not the obligation to either buy or sell something in the future. An option when bought is the right but not the obligation to either buy or sell something in the future. An option is a double derivative, being based on the underlying futures market, which in turn is based on the cash market. An option is a double derivative, being based on the underlying futures market, which in turn is based on the cash market.

© 2007 Thomson Delmar Learning, a part of the Thomson Corporation Option Basics The buyer of an option is buying the right, but not the obligation, to buy (call) or sell (put) something at some point in the future. The buyer of an option is buying the right, but not the obligation, to buy (call) or sell (put) something at some point in the future. The seller of an option has an obligation to perform if the buyer exercises the option. The seller of an option has an obligation to perform if the buyer exercises the option. If the buyer lets the option expire, the sellers obligation is dissolved. If the buyer lets the option expire, the sellers obligation is dissolved.(continued)

© 2007 Thomson Delmar Learning, a part of the Thomson Corporation Option Basics (continued) The sellers compensation for taking on the responsibility is called the premium. The sellers compensation for taking on the responsibility is called the premium. The price, if exercised, is called the strike price. The price, if exercised, is called the strike price. Options are strong contracts and can be retraded. Options are strong contracts and can be retraded. The initial buyer has three choices: exercise, let expire, or retrade by selling. The initial buyer has three choices: exercise, let expire, or retrade by selling.

© 2007 Thomson Delmar Learning, a part of the Thomson Corporation The Insurance Concept The owner of an insurance policy has purchased the right but not the obligation to use the benefits; the underwriter has agreed to the obligations of the coverage. The owner of an insurance policy has purchased the right but not the obligation to use the benefits; the underwriter has agreed to the obligations of the coverage. For this reason, options are often referred to as price insurance. For this reason, options are often referred to as price insurance. Options on futures are traded or offered on the exchanges at various strike prices at fixed intervals above and below the futures price with corresponding premiums. (See Figure 6-1, next slide.) Options on futures are traded or offered on the exchanges at various strike prices at fixed intervals above and below the futures price with corresponding premiums. (See Figure 6-1, next slide.)

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

Options: Strike Price At the money means that the strike price is the same as the underlying futures price. At the money means that the strike price is the same as the underlying futures price. In the money means that for puts (calls), the strike prices are above (below) the at-the-money price. In the money means that for puts (calls), the strike prices are above (below) the at-the-money price. Out of the money means that the strike prices for puts (calls) are below (above) the at-the-money strike price. Out of the money means that the strike prices for puts (calls) are below (above) the at-the-money strike price. At-the-money strike price is composed only of time value. At-the-money strike price is composed only of time value.

© 2007 Thomson Delmar Learning, a part of the Thomson Corporation Options The length of time to expiration of the option is directly related to the time value. The length of time to expiration of the option is directly related to the time value. The time value for options is the probability of a price move. The time value for options is the probability of a price move. Option premiums also have intrinsic value. Option premiums also have intrinsic value. –All in-the-money options have positive 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 variability of prices and length of time to maturity are critical. When assessing the time value of options, the variability of prices and length of time to maturity are critical.

© 2007 Thomson Delmar Learning, a part of the Thomson Corporation Options Pricing: The Premium The premium is simply the price at which the options contract trades. The premium is simply the price at which the 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 existsarbitragers keep markets honest and liquid. Other than buyers and sellers, a third party existsarbitragers keep markets honest and liquid. The Risk and Mitigation Profile process is the best approach for hedgers to determine whether any particular options contract meets their needs. The Risk and Mitigation Profile process is the best approach for hedgers to determine whether any particular options contract meets their needs.

© 2007 Thomson Delmar Learning, a part of the Thomson Corporation Black-Scholes Options Pricing Model The BSOPM was developed for European options on stocks, not commodity futures. The BSOPM was developed for European 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 model reacts to a change in any of the variables. Pit traders and arbitragers know how the model reacts to a change in any of the variables.(continued)

© 2007 Thomson Delmar Learning, a part of the Thomson Corporation Black-Scholes Options Pricing Model (continued) The BSOPM is dependent upon several assumptions: The BSOPM is dependent upon several assumptions: –All relevant markets are efficient. –Interest rates are constant and known. –Returns are lognormally distributed random variables. –No commissions are paid. –The option can only be exercised on expiration. The last assumption forces the model to specifically address European options. The last assumption forces the model to specifically address European options.(continued)

© 2007 Thomson Delmar Learning, a part of the Thomson Corporation Black-Scholes Options Pricing Model (continued) The BSOPM yields a theoretical premium. The BSOPM yields a theoretical premium. Market imperfections or differences between reality and assumption cause disparity between premiums. Relevant differences are: Market imperfections or differences between reality and assumption cause disparity between premiums. Relevant differences are: –The true underlying distribution of prices is not exactly lognormally distributed. –Borrowing and lending rates are different. –Volatility expectations differ among market participants. –The market is less liquid than it usually is or is theoretically expected to be. BSOPM remains the cornerstone of premium determinations. BSOPM remains the cornerstone of premium determinations.

© 2007 Thomson Delmar Learning, a part of the Thomson Corporation Option Pricing: The Greek Values The BSOPM is based on several major variables. The BSOPM is based on several major variables. These variables are explained in Figure 6-3 (see next slide). These variables are explained in Figure 6-3 (see next slide).

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

Buying Puts and Calls Buyers of options have at least seven different strike price/ premium combinations to choose from. Buyers of options have at least seven different strike price/ premium combinations to choose from. Option buying truncates the loss of trading at the premium level. (See Table 6-1, next slide.) Option buying truncates the loss of trading at the premium level. (See Table 6-1, next slide.) Buyers have unlimited gain potential with loss limited to the premium. Buyers have unlimited gain potential with loss limited to the premium. Sellers have limited gain potential with unlimited loss potential. Sellers have limited gain potential with unlimited loss potential. Buyers of call options are speculating that the price of the underlying futures contract will increase. Buyers of call options are speculating that the price of the underlying futures contract will increase. Buyers of put options are speculating that the price of the underlying futures contract will decrease. Buyers of put options are speculating that the price of the underlying futures contract will decrease.

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

Writing Puts and Calls To write an option is to accept the responsibility of performing in case the buyer decides to exercise the option. To write an option is to accept the responsibility of performing in case the buyer decides to exercise the option. Option writing truncates the gains of trading at the premium level. Option writing truncates the gains of trading at the premium level. Writers of options can write the option either covered or naked. Writers of options can write the option either covered or naked. –A covered writer will have the underlying futures contract the option is written against. –A naked writer does not have the underlying futures and is promising to provide one in case the buyer exercises the option.

© 2007 Thomson Delmar Learning, a part of the Thomson Corporation Writing Puts If a writer has a naked put, the writer will gain the premium if the price of the underlying futures increases. If a writer has a naked put, the writer will gain the premium if the price of the underlying futures increases. Table 6-3 shows the results of a price increase and decrease on a naked put. Table 6-3 shows the results of a price increase and decrease on a naked put. –Writers of naked puts are bullish. Table 6-4 shows the results of a put that is covered. The effects are the opposite of a naked put. Table 6-4 shows the results of a put that is covered. The effects are the opposite of a naked put. –Writers of covered puts are bearish. Put option writers will cover the option if they are bearish and leave the option naked if they are bullish. Put option writers will cover the option if they are bearish and leave the option naked if they are bullish. –Figures 6-8 and 6-9 illustrate these concepts.

© 2007 Thomson Delmar Learning, a part of the Thomson Corporation Writing Calls A call writer who is bullish will write the call covered. This writer earns the maximum possible when prices increases. A call writer who is bullish will write the call covered. This writer earns the maximum possible when prices increases. –Writer earns only the premium. A call writer who is bearish will leave the option naked. A call writer who is bearish will leave the option naked. –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.

© 2007 Thomson Delmar Learning, a part of the Thomson Corporation Writing versus Buying Options A bullish option writer can either write a call covered or write a put naked. A bullish option writer can either write a call covered or write a put naked. –These have the same returns. They are mechanically different, but alike financially. –Likewise bearish writers can write a call naked or write a put covered. Writing options covered or naked is simply done to reverse the direction of price expectation and not done for any risk management reasons. Writing options covered or naked is simply done to reverse the direction of price expectation and not done for any risk management reasons.(continued)

© 2007 Thomson Delmar Learning, a part of the Thomson Corporation Writing versus Buying Options (continued) The problem with writing options is risk management. The problem with writing options is risk management. –Losses are potentially unlimited. –Written options have limited value as a hedging tool. Buying options is a valid risk management tool because losses are limited and gains are unlimited. Buying options is a valid risk management tool because losses are limited and gains are unlimited. –The concept of counterbalance holds.

© 2007 Thomson Delmar Learning, a part of the Thomson Corporation Option Hedging Because gains are limited with written options, buying options will be used in simple hedging. Because gains are limited with written options, buying options will be used in simple hedging. Hedging with options creates the right but not the obligation to hedge with a futures contract. Hedging with options creates the right but not the obligation to hedge with a futures contract.(continued)

© 2007 Thomson Delmar Learning, a part of the Thomson Corporation Option Hedging (continued) Put Option Hedging Put Option Hedging –A corn producer could hedge his crop against falling prices by selling a corn futures contract, he could also do this by buying a put option on corn futures. If prices dropped, he could exercise the option and have a futures hedge; if prices go up, he can let it expire. –Table 6-7 shows these actions. Call Option Hedging Call Option Hedging –A feed company that has forward sold feed could use options to hedge as shown in Table 6-8.

© 2007 Thomson Delmar Learning, a part of the Thomson Corporation Floors and Ceilings with Option Hedging Tables 6-7 and 6-8 and Figures 6-12 and 6-13 illustrate the concept of price floors and ceilings. Tables 6-7 and 6-8 and Figures 6-12 and 6-13 illustrate the concept of price floors and ceilings. With a put option hedge in Figure 6-12, the price floor the producer will receive is $2.35 per bushel. With a put option hedge in Figure 6-12, the price floor the producer will receive is $2.35 per bushel. In Figure 6-13, the price ceiling the feed company will receive is $2.65 per bushel. In Figure 6-13, the price ceiling the feed company will receive is $2.65 per bushel. Hedging with futures provides a price floor, but at the same time provides a price ceiling. Hedging with futures provides a price floor, but at the same time provides a price ceiling.

© 2007 Thomson Delmar Learning, a part of the Thomson Corporation Hedging to a Certain Price/Cost This can be done because options have several strike prices to pick from when hedging. This can be done because options have several strike prices to pick from when hedging. Put option hedgers can subtract the premium from the strike price and derive the price floor, known as the target price. Put option hedgers can subtract the premium from the strike price and derive the price floor, known as the target price. Call option hedgers concerned about a price ceiling can find a target cost, which is the call strike price less the premium. Call option hedgers concerned about a price ceiling can find a target cost, which is the call strike price less the premium. –This is illustrated by Tables 6-9 and 6-10.

© 2007 Thomson Delmar Learning, a part of the Thomson Corporation Target Price Hedging A cattle producer can calculate his target price and have this valuable information before he has to make a decision. The rancher could buy an out-of-the-money put option at $96 to have a target price of $95.55/cwt. The ranchers gross profit will be $0.55/cwt as shown in Table A cattle producer can calculate his target price and have this valuable information before he has to make a decision. The rancher could buy an out-of-the-money put option at $96 to have a target price of $95.55/cwt. The ranchers gross profit will be $0.55/cwt as shown in Table 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.

© 2007 Thomson Delmar Learning, a part of the Thomson Corporation Target Cost Hedging Table 6-10 shows costs of feeder cattle relative to the initial strike price used as a hedge. A cattle feeder could use this to calculate her target cost. If she determines she can pay no more than $98/cwt, she could buy a call at the $97 strike price. The target cost will be $97.50/cwt. Table 6-10 shows costs of feeder cattle relative to the initial strike price used as a hedge. A cattle feeder could use this to calculate her target cost. If she determines she can pay no more than $98/cwt, she could buy a call at the $97 strike price. The target cost will be $97.50/cwt. The cattle feeder would achieve her strike price and reduce costs $.40/cwt. The cattle feeder would achieve her strike price and reduce costs $.40/cwt. This is a management decision that can be made prior to the production decision using target cost hedging. This is a management decision that can be made prior to the production decision using target cost hedging.

© 2007 Thomson Delmar Learning, a part of the Thomson Corporation Partial Coverage Hedging Sometimes only a certain level of protection is desired. This could be due to the cost of full coverage or the hedger is speculating that prices will move in her favor. Sometimes only a certain level of protection is desired. This could be due to the cost of full coverage or the hedger is speculating that prices will move in her favor. This would lead the buyer to purchase an option at a strike price that is farther out-of-the money. This would lead the buyer to purchase an option at a strike price that is farther out-of-the money. Table 6-13 illustrates this. Table 6-13 illustrates this.

© 2007 Thomson Delmar Learning, a part of the Thomson Corporation Option Multiple Hedging The relationship between the value of the option and the underlying futures price is called delta. The relationship between the value of the option and the underlying futures price is called delta. –Delta = change in the option premium/change in futures price. –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 only changes $0.50 with a delta of 0.5. –See Table To achieve a dollar equivalency between futures and options hedges requires a multiple. To achieve a dollar equivalency between futures and options hedges requires a multiple. –multiple = 1/delta (continued)

© 2007 Thomson Delmar Learning, a part of the Thomson Corporation Option Multiple Hedging (continued) Central idea behind deltas and multiples is to understand how the value of the option as a hedge changes as the futures price changes. Central idea behind deltas and multiples is to understand how the value of the option as a hedge changes as the futures price changes. Hedgers that desire to have a dollar value equivalency throughout the hedging period need to scale the hedge. Hedgers that desire to have a dollar value equivalency throughout the hedging period need to scale the hedge. –See Tables 6-15 and The process of scaling option hedges attempts to achieve delta neutral hedges. A true delta neutral hedge would achieve perfect dollar equivalency. The process of scaling option hedges attempts to achieve delta neutral hedges. A true delta neutral hedge would achieve perfect dollar equivalency.

© 2007 Thomson Delmar Learning, a part of the Thomson Corporation Final Word on Deltas Deltas of necessity have to be calculated after the fact. Thus they are always historic and static. Deltas of necessity have to be calculated after the fact. Thus they are always historic and static. Markets constantly change, resulting in hedges constantly needing to be scaled, thus increasing the cost. Markets constantly change, resulting in hedges constantly needing to be scaled, thus increasing the cost. A wise option hedger is aware of the importance of deltas and their limitations. A wise option hedger is aware of the importance of deltas and their limitations.

© 2007 Thomson Delmar Learning, a part of the Thomson Corporation Synthetic Futures Hedge Option buying combined with option writing can mimic a futures hedge. (See Table 6-17.) Option buying combined with option writing can 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 because the client has to pay two commissions for the options versus one for a futures hedge. This type of hedge is favored by some brokers because the client has to pay two commissions for the options versus one for a futures hedge. This type of hedge also parrots a futures hedge and costs more to place. It should be avoided. This type of hedge also parrots a futures hedge and costs more to place. It should be avoided. One popular type of a synthetic hedge involves buying out-of-the-money and selling in-the-money, earning an initial cash flow for the hedger. (See Table 6-18.) One popular type of a synthetic hedge involves buying out-of-the-money and selling in-the-money, earning an initial cash flow for the hedger. (See Table 6-18.)

© 2007 Thomson Delmar Learning, a part of the Thomson Corporation Options Hedge versus Futures Hedge Options are a superior way to hedge sometimes and inferior at other times. Options are a superior way to hedge sometimes and inferior at other times. Options are referred to as second best because an option hedge is less effective than an futures hedge when prices move against your cash position. Options are referred to as second best because an option hedge is less effective than an futures hedge 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 position, hedge with futures. If prices are forecasted to move in favor of the cash position, hedge with options. If prices are forecasted to move against the cash position, hedge with futures. If prices are forecasted to move in favor of the cash position, hedge with options.