Options Options ? Put Options ? Call Options ? Examples of derivatives Peter O’Grady

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Put Options Put Options

? Define S as the price of the underlying ? A put is a contract that gives the asset, and K as the . owner the right, but not the obligation, to ? In, out of, and at the money for puts sell an underlying asset, at a fixed price – In the money if S < K ($K), on (or on or before) a specific day. – Out of the money if S > K ? The put writer is obligated to buy the – At the money if S ~ K underlying asset, and pay $K for it. – Deep in (out of) the money if S << K (S >> K) ? Intrinsic value of a put = max(0,K-S) 3 4

Value of Put at (A.K.A. Profit Diagram -- Put Payoff Diagram) (Buying a Put)

P T Profit Just lower the payoff diagram by the put premium (price of put)to get the profit diagram

0 0 K S ST K T

put premium

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1 Example of a Put Option Example of a Put Option (cont.)

? buy a put option to purchase 100 Exxon shares Profit ($) – strike price = $70 3000 – price of an option to buy one share = $7 2500 2000 ? initial investment is 100 x $7 = $700 1500 ? The outcome 1000 Terminal price ($) 500 – Exxon’s share price is $55 at the expiration 0 40 50 60 70 80 90 100 – to the option for a gain of -700 ($70-$55) x 100 = $1,500 -1000 -1500 – the net gain = $1,500 - $700 = $800 Figure Profit from buying a Put Option on 100 Exxon share. Option price = $7; strike price = $70

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Profit Diagram – Put Insurance (Selling a Put) ? Insurance. If you own the underlying Profit asset, buying a put provides protection against the possibility that the underlying asset price will fall below $K. Of course, insurance costs 0 money (the put premium). K ST

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Call Options Call Options

? A is a contract that gives the ? In, out of, and at the money: Define S owner the right, but not the obligation, to as the price of the underlying asset, and buy an underlying asset, at a fixed K as the strike price. Then, for a call: price, on (or on or before) a specific – In the money if S > K day. – Out of the money if S < K ? The fixed price is called the strike price, – At the money if S ~ K or the exercise price. – Deep in (out of) the money if S >> K (S << K)

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2 Value of Call at Expiration, (A.K.A. Profit Diagram -- Long Call Payoff Diagram) (Buying a Call Option)

CT Just lower the payoff diagram Profit by the call premium (price of the option), to get the profit diagram

call premium 0 K ST 0 K ST

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Example of a Call Option Example of a Call Option (cont.)

? buy a call option to purchase 100 MSFT share – strike price = $52 Profit ($) – current share price = $50 1200 1000 – price of an option to buy one share = $2 800 ? initial investment is 100 x $2 = $200 600 400 ? The outcome 200 Terminal stock price ($)

– MSFT’s share price is $55 at the expiration 0 50 60 70 80 90 -200 – to exercise the option for a gain of ($55-$52) x 100 -400 = $300 -600 – the net gain = $300 - $200 = $100

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Example of a Call Option Example of a Call Option (cont.) ? buy a call option to purchase 100 IBM shares – strike price = $100 Profit ($) – current share price = $98 3000 – price of an option to buy one share = $5 2500 2000 ? initial investment is 100 x $5 = $500 (Worse case is 1500 that this will be lost) 1000 500 Terminal stock price ($) ? The outcome 0 90 100 110 120 130 – IBM’s share price is $115 at the expiration -500 – to exercise the option for a gain of -1000 -1500 ($115-$100) x 100 = $1,500 Figure Profit from buying a Call Option on 100 IBM share. Option – the net gain = $1,500 - $500 = $1,000 price = $5; strike price = $100

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3 Profit Diagram – Short Call Example of a Call Option (cont.) (Selling a Call Option)

Profit ($) 1000 Profit 500 0 Terminal stock price ($)

-500 90 100 110 120 130 -1000 -1500 0 -2000 K ST -2500 -3000 -3500

Figure Profit from writing a Call Option on 100 IBM share. Option price = $5; strike price = $100

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Example of a Put Option (cont.) Option Positions (cont.)

Profit Profit ($) Profit Terminal stock price ($) 700 0 X 40 50 60 70 80 90 100 -500 X ST ST -1000 -1500 (a) long call (b) short call -2000 Profit -2500 Profit -3000 -3500 -4000 ST X ST Figure Profit from writing a Put Option on 100 Exxon share. Option X price = $7; strike price = $70 (c) long put (d) short put 21 22

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