Investment Analysis and Portfolio Management Lecture 8

Options

Options An option is a contract that: Either Or Gives the right to buy an asset at a specific price within a specific time period but no obligation to buy This is a call option Or The right to sell an asset at a specific price within a specific time period but no obligation to sell This is a put option

Call Options A call option is the right to buy The contract specifies 1. The company whose shares are to be bought 2. The number of shares that can be bought 3. The purchase (or exercise or strike) price 4. The date when the right to buy expires (the expiration date)

Call Options European call: can only be exercised at the expiration date American call: can be exercised at any date up to the expiration date The premium is the price paid to buy the contract Exercise of the option does not imply that the asset is actually traded Because of transactions costs it is better for both parties to just transfer cash equal in value to what would happen if the asset were traded

Call Options A call option is purchased in expectation that it may be exercised Exercise depends on the exercise price and the price of the asset Will not exercise if the asset price is below the exercise price A European call is exercised if asset price is above exercise price at expiration date Purchase for less than its trading price With an American call when to exercise is a choice

Call Options Example On July 11 2003 Walt Disney Co. stock were trading at $20.56 Call options with a strike or exercise price of $22.50 traded with a premium of $0.05 These call options will only be exercised if the price of Walt Disney Co. stock rises above $22.50 This raises questions about the determination of the price And how the premium is affected by changes in the exercise price and stock price

Call Options Example A sells B the right to “buy 100 shares for £50 per share at any time in the next six months” If current price is £45 B must expect a price rise If price rises above £50 B will exercise the option and obtain assets with a value in excess of £50 If the price rises to £60 B purchases assets worth £6000 for £5000 If price falls below £50 B will not exercise the option

Call Options The return to A is the premium paid by B for the option If this is £3 per share B pays A £300 for the contract Final price £60 Profit of B is £6000 - £5000 - £300 = £700 Profit of A is £300 - £1000 = - £700 Final price £40 Profit of B is - £300 Profit of A is £300 The loss of A (or profit for B) is potentially unlimited The loss of B (profit for A) is limited to the premium

Call Options A profit is made on a call option if the underlying stock prices rises sufficiently above the exercise price to offset the premium Example Call options on Boeing stock with a strike price of $30.00 were trading at $5.20 on June 23, 2003 If a contract for 100 stock were purchased this would cost $520 In order to make a profit form this, the price on the exercise date must be above $35.20

Call Options Call options with lower exercise prices are always preferable and trade at a higher price A lower exercise price raises the possibility of earning a profit Profit is greater for any price of the underlying Example On June 23, 2003 IBM stock were trading at $83.18 Call options with expiry after the 18 July and a strike price of $80 traded at $4.70 Options with a strike price of $85 traded at $1.75

Put Options A put option is the right to sell The contract specifies 1. The company whose shares are to be sold 2. The number of shares that can be sold 3. The selling (or strike) price 4. The date when the right to sell expires (expiration date) European put: can only be exercised at the expiration date American put: can be exercised at any date up to the expiration date

Put Options An American put must be at least as valuable as the European given the flexibility in exercise Example On July 11 2003 Walt Disney Co. stock were trading at $20.56 Put options with an exercise price of $17.50 traded with a premium of $0.10 These will only be exercised if the price of Walt Disney Co. stock falls below $17.50

Put Options A put option is profitable if the price of the underlying asset falls far enough It must fall enough to cover the premium Example Put options on Intel stock with a strike price of $25.00 were trading at $4.80 on June 23, 2003 A contract for 100 stock would cost $480 To make a profit from this option the price of the underlying asset must be below $20.20

Put Options Example A sells B the right to sell 300 shares for £30 per share at any time in the next six months A must believe that the price will not fall below £30 B believes it will If the price falls below £30, B will exercise the option and obtain a payment in excess of the value of the assets

Put Options If the price goes to £20 B will receive £9000 for assets worth £6000 If price stays above £30 B will not exercise the option The return to A is the premium paid by B for the option If this is £2 per share B pays A £600 for the contract

Put Options Final price £20 Profit of B is £9000 - £6000 - £600 = £2400 Profit of A is £6000 + £600 - £9000 = - £2400 Final price £40 Profit of B is - £600 Profit of A is £600 The loss to A (or profit to B) is limited to the exercise price The loss of B (profit to A) is limited to the premium

Put Options The higher is the strike price the more desirable is a put option This is because a greater profit will be made upon exercise Example On June 23, 2003 General Dynamics stock were trading at $73.83 Put options with expiry after the 18 July and a strike price of $70 traded at $1.05 Those with a strike price of $75 traded at $2.95

Trading Options Options are traded on a range of exchanges Chicago Board Options Exchange, the Philadelphia Stock Exchange, the American Stock Exchange and the Pacific Stock Exchange Eurex in Germany and Switzerland and the London International Financial Futures and Options Exchange Options contracts are for a fixed number of stock An options contract in the US is for 100 stock

Trading Options Exercise prices are set at discrete intervals $2.50 interval for stock with low prices Up to $10 for stock with high prices On introduction of an option two contracts are written One with an exercise prices above the stock price One with an exercise price below the stock price If the stock price goes outside this range new contracts can be introduced As each contract reaches its date of expiry new contracts are introduced for trade

Trading Options Quotes of trading prices for options contracts can be found in The Wall Street Journal and the Financial Times Quote the call and put contracts with exercise prices just above and just below the closing stock price of the previous day Price quoted is for a single share More detailed information can also be found on Yahoo Lists the prices for a range of exercise values, the volume of trade, the number of open contracts

Trading Options Market makers can be found on each exchange to ensure that there is a market for the options The risk inherent in trading options requires that margin payments must be must in order to trade

Valuation of Options The value of an option is related to the value of the underlying security At expiration Consider a call option, exercise price £100 Asset price below £100: option worthless Asset price above £100: can profit from owning option, so valuable

Valuation of Options The value (which is equal to the "fair" price) at expiration is given by Vc = max{S – E, 0} Vc is the value of the call option, S the price of the underlying asset and E the exercise price

Valuation of Options Example On June 26 2003 GlaxoSmithKline stock was trading at $41 The exercise prices for the option contracts directly above and below this price were $40 and $42.50 The table displays the value at expiry for these contracts for a selection of prices of GlaxoSmithKline stock at the expiration date S 37.50 40 41 42.50 45 47.50 max{S-40,0} 1 2.50 5 7.50 max{S-42.50,0}

Valuation of Options The profit, Pc, from holding the option is Pc = Vc – V0 = max{S – E, 0}- V0 = max{S – E - V0, -V0} V0 is the price (premium) paid for the call option

Valuation of Options Consider a put option, exercise price £100 This is worthless if the price of the asset is greater than £100 It is valuable if the price of the asset is less than £100

Valuation of Options The value or fair price at expiration is given Vp = max{E – S, 0} The value is whichever is larger of 0 and E – S

Valuation of Options Shares in Fox Entertainment Group Inc. traded at $29.72 on 7 July 2003 The expiry value of put options with exercise prices of $27.50 and $30.00 are given in the table for a range of prices S 20 22.50 25 27.50 30 32.50 max{27.50-S,0} 7.50 5 2.50 max{30-S,0} 10

Valuation of Options The profit from purchasing it is Pp = Vp - V0p = max{E - S, 0}- V0p = max{E – S - V0p, -V0p} V0p is the purchase price of the put option

Combining Puts and Calls Combinations of puts and calls engineer different structures of payoffs The straddle involves buying a put and a call on the same stock If these have the same exercise price, the profit is = max{E - S, 0} + max{S - E, 0} - V0p - V0c