Chapter 14 Options Keith Pilbeam Finance and Financial

Chapter 14 Options Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

Learning Objectives Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

Options � options – a special type of financial asset that give the holder the right but not the obligation to buy or sell an underlying security at a predetermined price � First traded in Chicago in 1972 � A decade later in 1982 London International Financial Futures Exchange (LIFFE) � ICE Futures Europe is now Europe’s largest Exchange � most popular options types: § interest rate options § currency options § stock index options § individual stock options Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

The Growth of Options Markets � Turnover of options contracts traded on international exchanges (contracts in millions) Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

Options Contracts - Jargon � an option contract involves two parties: writer – the person who sells a call or put option contract holder – the person who buys a call or put option contract � holder the right but not the obligation to buy an underlying asset/security at a predetermined exercise price at some time in the future put option – a contract that gives the holder the right but not the obligation to sell an underlying asset/security at a � exercise price/strike price – the predetermined exercise price at some price at which an option holder has the time in the future right to sell or buy an underlying asset/security � American option – a contract that can be exercised at any time up until its maturity date � option premium – a fee that is paid by an option holder to the option writer in � European option – a contract that can only be exercised on the maturity date return for the right to buy or sell an underlying asset/security at a given � The underlying – the underlying assets exercise price and quantity the holder has the right to buy or sell � call option – a contract that gives the Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

Call and Put Premiums � Call and Put options on Company ABC Shares Consider the Dec 2010 call price of 18 pence at a strike price of 540 pence. The price paid for the call option of 18 pence is known as the option premium, and the buyer of such a call option would have the right but not the obligation to buy 1, 000 Company ABC shares at a price of 540 pence in December for a cost of 18 pence per share (that is, a total cost of £ 180). Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

Positions in Options � There are 4 basic positions that can be taken on an options contract: 1. long call – buying a call option 2. short call – selling a call option 3. long put – buying a put option 4. short put – selling a put option Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

A Call Option Contract � Consider the underlying asset as 1, 000 shares in British Petroleum which are currently � � � � priced at 525 pence. Mr A buys a call option with a strike price of 540 for March 2010 for an option premium of 18 pence a share (a total of £ 180, that is £ 0. 18 x 1000). Mr A has purchased the right to buy from the writer of the option 1, 000 shares in BP at a price of 540 per share. The maximum amount that the option holder can lose is £ 180, while the maximum profit the option writer can make is £ 180. Scenario 1: price in March is below 540 - the holder will not exercise the option (holder will have lost the £ 180 premium paid, with the writer making £ 180) Scenario 2: price in March is above 540, then the holder will exercise the option, since it will pay him to buy the shares at 540 pence and sell them spot at a higher price. Scenario 2 a: If the price rises above 540 pence but to less than 558 pence: loss from exercising the option but less than not exercising at all. Scenario 2 b: A future spot price of 558 pence, the option holder breaks even. Scenario 2 c: If the price rises above 558 pence the holder will exercise his option at a profit. Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

A Call Option Contract Holder Max loss is -£ 180 (option premium) Max profit limitless Writer Max profit is £ 180 Max loss is limitless Asymmetrical profit and loss profile Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

The Pay-offs from the Long call and Short call Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

A Put Option Contract � Consider the underlying asset as 1, 000 shares in BP which are currently priced at 525 � � � � pence. Mr A buys a put option with a strike price of 540 for March 2010 for an option premium of 38 pence a share (a total of £ 380, that is £ 0. 38 x 1000). Mr A has purchased the right to sell to the writer of the option 1, 000 shares in British Petroleum at a price of 540 per share. Scenario 1: price in March is above 540 - the holder will not exercise the option (holder will have lost the £ 380 premium paid, with the writer making £ 380) Scenario 2: price in March is less 540, then the holder will exercise the option, since it will pay him to sell the shares at 540 pence and buy them spot at a higher price. Scenario 2 a: If the price falls below 540 pence but to greater than 5 o 2 pence - loss from exercising the option but less than not exercising at all. Scenario 2 b: A future spot price of 502 pence will mean the option holder breaks even. Scenario 2 c: If the price falls below 502 pence the holder will exercise his option at a profit. Consider a fall at 400 – he will exercise the right to sell the shares at 540 making 140/share less the option premium of 38/share = net profit of 102/share or £ 1020 total. Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

A Put Option Contract Holder Max loss is -£ 380 Max profit limitless Writer Max profit is £ 380 Max loss is limitless Asymmetrical profit and loss profile Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

Profit or Loss from a Put Option contract 502 Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

Payoffs of European Options a call option a put option � A buys a call option on 1, 000 BP � B buys a put option on 1, 000 BP shares (SBP) § current share price=0. 525 § strike price=0. 540 § maturity=March 2010 � possible scenarios at expiry: § SBP <540: the holder will not exercise the option, losing the premium paid £ 180 § 540< SBP <558: the holder will exercise the option, making an overall loss § SBP >558: the holder will exercise the option, making a profit from the strategy � the holder of a call option has a substantial upside potential profit with limited maximum downside shares (SBP) § current share price=0. 525 § strike price=0. 540 § maturity=March 2010 � possible scenarios at expiry: § SBP >540: the holder will not exercise the option, losing the premium paid £ 380 § 502< SBP <540: the holder will exercise the option, making an overall loss § SBP <502: the holder will exercise the option, making a profit from the strategy � the holder of a put option has a maximum loss equal to the option premium and substantial upside potential Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

“Writing naked” vs “Writing covered” � ‘writing naked’: when you write options on a security that you do not own - quite risky as the share price can go up and up in value increasing the writer’s loss in the process. � ‘writing covered’: the writer owns a quantity of the shares on which he is writing the call option. � NAKED: The holder has paid a premium of £ 180 to buy 1, 000 shares at strike price of 540 pence and the writer has received £ 180 which is the maximum profit the writer can make. If the share price rises to 800 pence we have seen that the writer will lose £ 2, 420. � COVERED: Suppose the writer owns 900 shares (worth 900 x£ 5. 25=£ 4, 725). If the share rises in price to 800, then the 900 shares will be worth (900 x£ 8=£ 7, 200). The writer thus sees an appreciation of £ 2, 475 which more than covers his loss of £ 2, 420 from having written the call options. Fully covered! � If he had in his hands only 500 shares – partially covered! Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

“Writing covered” as a Strategy � If the fund manager owns 1000 shares in British Petroleum as part of his ‘core � � portfolio’ and does not expect them to change much between August and March then he could write some call options on the share. Consider three cases: (a) price remains at £ 5. 25; (b) falls £ 5. 15; (c) rises £ 8. 00 If the share remains at £ 5. 25 between August and March then the shares he owns will still be worth £ 5, 250, but he will have a useful profit of £ 180 from having written the call options which expire worthless to the holder. If the shares fall in price to £ 5. 15 then his shares will be worth £ 5, 150 which is £ 100 less but his profit of £ 180 from writing the call option will mean his net position in British Petroleum is worth £ 5, 150 plus the profit from writing the call of £ 180 which is £ 5, 330. If the share rises to £ 8 then his shares are worth £ 8, 000 but the loss of £ 2420 from writing the call options will mean his net position in BP is worth only £ 5, 580. This is an improvement over £ 5, 250 but far less than the £ 8, 000 value he would have had if he had not written the call option Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

Stock Index Options The FTSE 100 index options are valued at £ 10 the FTSE 100 cash index level, with expiration on the third Friday of the month. The premium is quoted in pence per unit of the contract with each full point movement in the index being worth £ 10. For example, if someone buys a call contract on the FTSE 100 for December at 6900 for 235 points, or a premium of £ 2, 350, the holder has the right between August and the expiration day in December to buy the index at a level of 6, 900. Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

Stock Index Options � allow to take positions on the movement of a broad market index � stock index option – a contract giving the holder the right but not the obligation to buy or sell a stated stock index at a particular price at some time in the future � this type of options work on a cash settlement basis since the actual delivery of the many shares that comprise the index would be impractical and costly � example: long FTSE 100 call if the FTSE 100 spot price Dec 7200, then the call option will be exercised and the writer has to pay the holder the difference between the spot price of the index and the strike multiplied by £ 10: (7200 -6, 900)*10=£ 3000 § therefore, the net profit of the holder is: £ 3000 -£ 2350=£ 650 § Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

Stock Index Options Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

Interest Rate Options � interest rate option – a contract giving the holder the right but not the obligation to lend (call) or borrow (put) a stated nominal notional amount, for a given period of time at a predetermined rate of interest � based upon the movements in debt instruments � especially popular in the USA – ‘options on physicals’ Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

Interest Rate Options � Example: buying a short sterling call for 4 basis points � this contract gives a right to lend £ 500 K at 5% (100 -95. 00) for 3 months from Nov § each tick movement is worth: £ 500, 000× 0. 0001×(3/12)=£ 12. 50 § the cost of call: 4×£ 12. 50=£ 50 § if the contract rises to 95. 5 by Nov (lowered interest rate), then the holder is entitled to a gain of 50 bps and his margin account will be credited with: 50×£ 12. 50=£ 625 § the net profit of the holder is: 625 -50=£ 575 If interest rates have risen to 5. 50% the contract is trading at 94. 50, then the contract will not be exercised and the holder will lose the premium paid of £ 50. What if interest rates have risen to 5. 50%? Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

Currency Options � first traded on the Philadelphia Stock Exchange in the early 1980 s � currency option – a contract giving the holder the right but not the obligation to buy or sell a certain amount of the underlying currency at a given exchange rate underlying currency is £ � Example: CME American $/£ options £ 62, 500 ($6. 25 per tick) § the spot exchange rate 31 August is $1. 25/£ 1 § the total premium payable on a Dec call at $1. 27/£ 1: $0. 03× 62, 500=$1875 Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

Currency Options � If the future spot exchange rate is less than $1. 27/£ 1, then it does not pay the buyer of the option to exercise his option because it is cheaper to buy pounds in the spot market and he will lose the premium paid of 3 US cents per pound. � If the future spot exchange rate is between $1. 27/€ 1 and $1. 30/£ 1 it will pay the buyer of the option to exercise the option although he will make a loss equating to the future spot price less the strike price and option premium. � If the future spot price is above $1. 30/£ 1, the call option will make a net profit for the holder. � The writer of the option makes a profit or loss that is the mirror image of the profit and loss profile of the holder. Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

The Uses of Options provide a cheap and flexible way to control some significant risks and to take highly leveraged speculative positions Options attract: 1. hedgers 2. arbitrageurs 3. speculators Hedgers: basic motive is to control their risk exposure Arbitrageurs: try to exploit possible divergences between the value of calls and puts (try to make profitable, risk-free trades until the discrepancy is eliminated see Put-Call parity) Speculators: basic motive is to make profits by taking risk positions in the instruments. Attractive, since a small initial premium gives the opportunity for very large returns Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

Examples: Hedging the risk 1. Hedging the risk of an adverse equity price movement target: a pension fund with a portfolio of shares needs to realize £ 50 m in three months time § risk: the stock market might fall within 3 months, requiring more shares to be sold to realize the necessary amount § solution: purchase put options on stock market index; if market falls exercise the right 2. Hedging the risk of an adverse interest rate movement § target: a company requires $20 m bank loan in six months time; interest rates are 5% § risk: the company is afraid that the interest rates might rise to 6% or 7% in six months’ time § solution: purchase put options on a bond index; if interest rates rise, bond prices will fall and the company can exercise the right to sell bonds at a predetermined price. 3. Risk-averse foreign exchange movement § target: a UK firm is borrowing for one year $20 m at a fixed 7%; require US$ interest and principal repayments § risk: the company is afraid that the pound might be depreciated against dollar § solution: purchase dollar calls, i. e the right to buy dollars at a predetermined price; if dollar depreciates the firm will be able to buy dollars spot. § Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

Examples: Speculation using a share option § current share price of Company ABC is £ 2 § investor with £ 1000 is confident that it will rise to £ 3 per share in 6 months time § 6 -month call on this share at strike £ 2. 20 is currently £ 0. 10 per share § strategy 1: buy now 500 shares at £ 2, sell at £ 3 in 6 months, net profit=£ 500 § strategy 2: buy now 10 calls of 1, 000 shares (i. e. the right to buy 10, 000 shares at £ 2. 20), exercise them in 6 months, net profit=£ 7, 000 § Net profit comes from the fact that he will exercise the right to buy the shares at £ 22, 000 and immediately sell them at £ 30, 000 (8, 000 diff) less the option premium of 1, 000. § § This spectacular profit comes at a high risk. Consider if price of shares goes up to £ 2. 10 By buying and selling he makes a profit of £ 50 By buying the option contract he losses all his money (£ 1, 000) Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

Relation to Futures Options both parties are obliged to transact the buyer is not obliged to transact the buyer and seller have a simple pound-for-pound gain/loss scenario - the maximum loss of a buyer (maximum gain of the writer) is limited to the option premium - the maximum gain of the holder (loss of the writer) is potentially unlimited useful instruments for hedging against symmetric risks useful instruments for hedging against asymmetric risks Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

Currency Option vs a Forward Contract � Hedging § in Jan a US company orders € 1 m goods from Germany to be delivered in 1 year, paying cash upon delivery; the euro depreciated from $1. 50/€ 1 to $1. 28/€ 1 over the last year, the company wishes to protect itself from any rise in the euro § one-year forward/futures rate is $1. 25/€ 1 – provides the firm with full certainty over the future cost of € 1 m § one-year call is sold at a premium $80, 000 which gives the holder the right to exchange $1. 25/€ 1 – enables the firm to fix the maximum payable price and also to take advantage of a favourable movement in the exchange rate Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

Currency Option versus a Forward Contract for Hedging Forward Advantage: Fully covered for any movement and know $ cost worth certainty Disadvantage: cannot take advantage if dollar appreciates Both help to hedge the risk of an increase fully and they reduce uncertainty compared to doing nothing! Option Advantage: can take advantage if dollar appreciates Disadvantage: the additional cost of the option premium of $80, 000 Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

Currency Option vs a Forward Contract � Speculation § the euro depreciated from $1. 50/€ 1 to $1. 28/€ 1 over the last year, but the speculator expects that the euro is likely to appreciate to $1. 50/€ 1 § The speculator has $80, 000 available for speculative purposes § one-year forward/futures rate is $1. 25/€ 1 – if the forecast of the speculator is correct his net profit will be: ($80, 000/1. 25)*1. 50 -$80, 000=$16, 000 § one-year call is sold at a premium $80, 000 which gives the holder the right to exchange $1. 25/€ 1 – if the speculator is right then his net profit will be $1, 500, 000 -$1, 250, 000 -$80, 000=$170, 000 Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

Currency Option vs a Forward Contract Forward Symmetric Less Dramatic profit and loss profile Option Asymmetric Excessive wins BUT also Large potential loss Of all the premium paid! Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

Option Strategies � The risk-returns profiles of options allows to use them in numerous ways for risk management. There are two well-known strategies which are useful when the investor believes that the share price will move but is unsure of the direction: � straddle – an option strategy that involves the simultaneous purchase of call and put options on a share at the same strike price and the same time to expiration § e. g. : long Mar calls and puts at 540 ⟶ max loss = 180+380=£ 560 � strangle – an option strategy that involves the simultaneous purchase of call and put options on a share at different strike prices and the same time to expiration § e. g. : long Mar calls at 540 and Mar puts at 520 ⟶ max loss = 180+270=£ 450 Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

Straddle Strategy straddle – an option strategy that involves the simultaneous purchase of call and put options on a share at the same strike price and the same time to expiration Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

The Profit and Loss from a Long Straddle Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

Strangle Strategy � Consider again options on Company ABC � strangle – an option strategy that involves the simultaneous purchase of call and put options on a share at different strike prices and the same time to expiration § e. g. : long Mar calls at 540 and Mar puts at 520 ⟶ max loss = 180+270=£ 450 Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

Straddle Strategy Long Mar calls and puts at 540 ⟶ Total Premium £ 180+£ 380=£ 560 Mx loss occurs if future spot price = strike price Basically it is a bet on the volatility of the share. Note expiration inside 484 to 596 there is a loss to the long straddle

Other Strategies • There are numerous other well known strategies that can be pursued using combinations of options to change the profit/loss profile • ‘strap’ (two calls and one put with the same expiry date, although exercise prices can differ) • ‘strip’ (one call and two puts with the same expiry date, although exercise prices can differ). • In addition an investor can have both a long and a short position in two or more option contracts. • ‘long butterfly’ strategy the investor has a long call with a low exercise price (X 1), two short calls with a middle exercise price (X 2) and a long call with a high exercise price (X 3), where we have X 1 < X 2 < X 3 and all options contracts have the same expiry date; it has a similar risk–return profile to a short straddle, but caps the potential downside losses. • ‘horizontal spreads’ and ‘calendar spreads’ using similar strike prices but different expiry dates • ‘diagonal spreads’ using both different expiry dates and different strike prices. • www. theoptionsguide. com has many strategies, graphs and explanations! Keith Pilbeam ©: Finance and Financial Markets 4 th Edition

Exotic Options � chooser option: allows the holder to convert from one type of option to � � � another at a certain point prior to expiration (usually choosing between call and put) average rate option: the settlement is based upon the difference between the strike price and the average price of the stock on certain dates barrier options: a number of different options whose payoff pattern and even survival depends not only on the underlying price of the security, but also on whether the security reached a predetermined barrier at any time during the life of the option compound option: an option on an option lookback option: the payout is determined by using the highest intrinsic value of the underlying security over the life of an option quanto option: the foreign exchange risks in an underlying security have been eliminated warrant: the right to buy or sell an underlying instrument at a given price and time, or at a series of prices and times (usually on a newly issued security) Keith Pilbeam ©: Finance and Financial Markets 4 th Edition