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To hedge risksTo speculate (take a view on the future direction of the market)To lock in an arbitrage profitTo change the nature of a liabilityTo change the nature of an investment without incurring the costs of selling one portfolio and buying another
A futures contract is an agreement to buy or sell an asset at a certain time in the future for a certain priceBy contrast in a spot contract there is an agreement to buy or sell the asset immediately (or within a very short period of time)
The futures prices for a particular contract is the price at which you agree to buy or sellIt is determined by supply and demand in the same way as a spot price
Traditionally futures contracts have been traded using the open outcry system where traders physically meet on the floor of the exchangeIncreasingly this is being replaced by electronic trading where a computer matches buyers and sellers
Agreement to:buy 100 oz. of gold @ US$600/oz. in December (NYMEX) sell £62,500 @ 1.9800 US$/£ in March (CME)sell 1,000 bbl. of oil @ US$65/bbl. in April (NYMEX)
The over-the counter market is an important alternative to exchangesIt is a telephone and computer-linked network of dealers who do not physically meetTrades are usually between financial institutions, corporate treasurers, and fund managers
Forward contracts are similar to futures except that they trade in the over-the-counter marketForward contracts are popular on currencies and interest rates
A call option is an option to buy a certain asset by a certain date for a certain price (the strike price)A put option is an option to sell a certain asset by a certain date for a certain price (the strike price)
Chicago Board Options ExchangeAmerican Stock ExchangePhiladelphia Stock ExchangeInternational Securities ExchangeEurex (Europe)and many more (see list at end of book)
A futures/forward contract gives the holder the obligation to buy or sell at a certain priceAn option gives the holder the right to buy or sell at a certain price
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Three Reasons for Trading Derivatives:Hedging, Speculation, and Arbitrage
Hedge funds trade derivatives for all three reasons (See Business Snapshot 1.1)
When a trader has a mandate to use derivatives for hedging or arbitrage, but then switches to speculation, large losses can result. (See Barings, Business Snapshot 1.2)
A US company will pay £10 million for imports from Britain in 3 months and decides to hedge using a long position in a forward contractAn investor owns 1,000 Microsoft shares currently worth $28 per share. A two-month put with a strike price of $27.50 costs $1. The investor decides to hedge by buying 10 contracts
An investor with $2,000 to invest feels that Amazon.com’s stock price will increase over the next 2 months. The current stock price is $20 and the price of a 2-month call option with a strike of $22.50 is $1What are the alternative strategies?
Suppose that:The spot price of gold is US$600The quoted 1-year futures price of gold is US$650The 1-year US$ interest rate is 5% per annumNo income or storage costs for gold
Suppose that:The spot price of gold is US$600The quoted 1-year futures price of gold is US$590The 1-year US$ interest rate is 5% per annumNo income or storage costs for gold
Suppose that:The spot price of oil is US$70The quoted 1-year futures price of oil is US$80The 1-year US$ interest rate is 5% per annumThe storage costs of oil are 2% per annum
Suppose that:The spot price of oil is US$70The quoted 1-year futures price of oil is US$65The 1-year US$ interest rate is 5% per annumThe storage costs of oil are 2% per annum
A long futures hedge is appropriate when you know you will purchase an asset in the future and want to lock in the priceA short futures hedge is appropriate when you know you will sell an asset in the future & want to lock in the price
Companies should focus on the main business they are in and take steps to minimize risks arising from interest rates, exchange rates, and other market variables
Shareholders are usually well diversified and can make their own hedging decisionsIt may increase risk to hedge when competitors do notExplaining a situation where there is a loss on the hedge and a gain on the underlying can be difficult
Choose a delivery month that is as close as possible to, but later than, the end of the life of the hedgeWhen there is no futures contract on the asset being hedged, choose the contract whose futures price is most highly correlated with the asset price. There are then 2 components to basis
Proportion of the exposure that should optimally be hedged is
where σS is the standard deviation of ΔS, the change in the spot price during the hedging period, σF is the standard deviation of ΔF, the change in the futures price during the hedging periodρ is the coefficient of correlation between ΔS and ΔF.
Desire to be out of the market for a short period of time. (Hedging may be cheaper than selling the portfolio and buying it back.)Desire to hedge systematic risk (Appropriate when you feel that you have picked stocks that will outpeform the market.)
We can use a series of futures contracts to increase the life of a hedgeEach time we switch from 1 futures contract to another we incur a type of basis risk
The commodity Futures Trading Commission authorized the trading of options on futures on an experimental basis in 1982.Permanent trading wa approved in 1987.The popularity of the contract with investors has grown very fast.
Expiration Months
Futures options are referred to by the delivery month of the underlying futures contract---not by the expiration month of the option.Most futures options are American.The expiration date of a futures option contract is usually on, or a few days before, the earliest delivery date of the underlying futures contract.
An investor buys a July call futures option contract on gold. The contract size is 100 ounces. The strike price is 900.The investor exercises when the July gold futures price is 940 and the most recent settlement price is 938.The outcome
1. The investor receives a cash amount equal to (938-900)*100=$3,800
2. The investor receives a long futures contract.3. The investor closes out the long futures contract
immediately for a gain of (940-938)*100=$2004. Total payoff = $4,000
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Example 16.2 Mechanics of put futures options
An investor buys a September put futures option contract on corn. The contract size is 5,000 bushels. The strike price is 300 cents.The investor exercises when the September corn futures price is 280 and the most recent settlement price is 279.The outcome
1. The investor receives a cash amount equal to (3.00-2.79)*5,000=$1,050
2. The investor receives a short futures contract.3. The investor closes out the short futures contract
immediately for a loss of (2.79-2.80)*5,000= -$504. Total payoff = $1,000
Potential Advantages of FuturesOptions over Spot Options
Futures contract may be easier to trade than underlying assetExercise of the option does not lead to delivery of the underlying asset Futures options and futures usually trade in adjacent pits at exchangeFutures options may entail lower transactions costs
European Spot Options and European Futures Options
The payoff from a European call option with strike price K on the spot price of an asset is
Max (ST - K,0), where ST is the spot price at the option’s maturity.The payoff from a European all option with the same strike price on the futures price of the asset is
Max (FT - K, 0), where FT is the futures price at the option’s maturity.
If the futures contract matures at the same time as the option, then FT = ST, and the two options are equivalent.
A futures contract requires no initial investment.In a risk-neutral world the expected profit from holding a position in an investment that costs zero to set up must be zero.The expected growth rate of the futures price is therefore zero.The futures price can therefore be treated like a stock paying a dividend yield of r.This is consistent with the results we have presented so far (put-call parity, bounds, binomial trees).
Black’s Model Compare equations on p.28 and equations on p.29, one clue could be derived.The two sets of equations are identical when we set q = r.Fischer Black was the first to show that European futures options can be valued using equations on p.28 with q = r and S0 replaced by F0.
European futures options and spot options are equivalent when future contract matures at the same time as the option.This enables Black’s model to be used to value a European option on the spot price of an asset
Consider a European put futures option on crude oil. The time to the option’s maturity is four months, the current futures prices is $60, the exercise price is $60, the risk-free interest rate is 9% per annum, and the volatility of the futures price is 25% per annum. The put price is given by
Valuation of a European futures option (continued)
The put price p is $3.35.
78
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Valuing a spot option using futures prices
Consider a 6-month European call option on spot gold6-month futures price is 930, 6-month risk-free rate is 5%, strike price is 900, and volatility of futures price is 20%Value of option is given by Black’s model with F0=930, K=900, r=0.05, T=0.5, and s=0.2It is 44.19
American Futures Option Prices vs American Spot Option Prices
If futures prices are higher than spot prices (normal market), an American call on futures is worth more than a similar American call on spot. An American put on futures is worth less than a similar American put on spot.When futures prices are lower than spot prices (inverted market) the reverse is true.
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Futures Style Options (page 353-54)
A futures-style option is a futures contract on the option payoffSome exchanges trade these in preference to regular futures optionsThe futures price for a call futures-style option is
The futures price for a put futures-style option is
A call is an option to buyA put is an option to sellA European option can be exercised only at the end of its lifeAn American option can be exercised at any time
Most exchanges use market makers to facilitate options tradingA market maker quotes both bid and ask prices when requestedThe market maker does not know whether the individual requesting the quotes wants to buy or sell
Margins are required when options are soldFor example when a naked call option is written the margin is the greater of:1 A total of 100% of the proceeds of the sale plus
20% of the underlying share price less the amount (if any) by which the option is out of the money
2 A total of 100% of the proceeds of the sale plus 10% of the underlying share price
Warrants are options that are issued (or written) by a corporation or a financial institutionThe number of warrants outstanding is determined by the size of the original issue & changes only when they are exercised or when they expire
Warrants are traded in the same way as stocks The issuer settles up with the holder when a warrant is exercisedWhen call warrants are issued by a corporation on its own stock, exercise will lead to new treasury stock being issued
They become vested after a period of time (usually 1 to 4 years)They cannot be soldThey often last for as long as 10 or 15 yearsAccounting standards are changing to require the expensing of executive stock options
Very often a convertible is callableThe call provision is a way in which the issuer can force conversion at a time earlier than the holder might otherwise choose