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11-1 Put and Call Options Chapter 11

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11-2 A call option is the right to buy an underlying security at an exercise (strike) price during a stated time interval. C = Market value of the call option. P = Market value of the underlying asset. E = Exercise price (strike price). Call Options

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11-3 Expiration Would like to find value here 0 But first need to determine value here

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11-4 Value of call option at expiration, E = $100 P E e.g., P = 90P = 100P = 110 C = 0C = 0C = P – E e.g., C = 10 out-of-the-moneyat-the-moneyin-the-money

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11-5 If C < P - E at expiration Suppose P = 110, E = 100, C* = 6. Arbitrage: Buy Call-6 Exercise-100 Sell Underlying+110 Arbitrage Profit+4 Arbitrage Guarantees That C = P – E

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11-6 Case of C > P – E: Suppose P = 110, E = 100, C** = 17. Arbitrage: Write Call+17 Exercised+100 Buy Underlying-110 Arbitrage Profit+7

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11-7 Value of call option before expiration, E = $100 P E e.g., P = 90P = 100P = 110 C > 0C > 0C > P – E e.g., C > 10

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11-8 Arbitrage Feasible call prices C P – E P P E Call Option Bounds

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11-9 Time 0 Write Call+C Buy Underlying-P C – P > 0 Expiration P E Sell Underlying+P+P = E Call Exercised+E Net+P+E+E Arbitrage if C > P

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11-10 Expiration Determine Profit or Loss Overlooking Dividends and Interest Take a position 0 Close entire position Profit Profiles

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11-11 Expiration Buy or Call -4 0 Close: Exercise if in-money. Let expire if out-of-money.

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11-12 -4 Price of underlying at expiration 98100102104 Buy call-4 Exercise call at expiration Sell underlying acquired from exercise Net profit = - C -4 Net profit = – C – E + P -2 0 -4 -100 +102 -4 -100 +104 Profits or Losses for Call Buyer

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11-13 P exp E Payoff Function: Buy Call E + c Breakeven – c– c + [P exp – E] 0 – c + –

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11-14 $ P at Expiration + Profit Call in-money 0 - Loss -4 Call out-of-money 100 E 104 Buy Call Profit Profile for Buying a Call -C -C+ [P–E]

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11-15 Price of underlying at expiration 98100102104 Write call+4 Sell underlying Buy underlying Net profit = + C Net profit = + C + E – P +2 0 +4 +100 -102 +4 +100 -104 +4 Profits or Losses for Call Writer

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11-16 $ P at Expiration + Profit 0 - Loss +4 104 Write Call $ P at Expiration + Profit Call in-money 0 - Loss Call out-of-money 100 E 104 Profit Profile for Writing a Call +C+C – [P-E]

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11-17 P exp E Payoff Function: Write Call E + c Breakeven + c+ c – [P exp – E] 0 + c + –

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11-18 Price of underlying at expiration 98100102104 Buy underlying-100 Write call+4 Sell underlying at exercise price when call is exercised Sell underlying at market+100 price Net profit+4 -100 +4 +100 +4 -100 +4 +100 +4 -100 +4 +98 +2 Profits or Losses from Writing a Covered Call

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11-19 $ + Profit 0 - Loss C Write covered call Buy underlying security Call in-moneyCall out-of-money 100 E Underlying asset at expiration Profit Profile for Writing a Covered Call Option

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11-20 Profit 0 Loss +4 Write call Buy underlying security Call in-moneyCall out-of-money 100 E Underlying asset at expiration 104 -4 Buy call Profit Profile for Call Option

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11-21 Expiration A put option is the right to sell the underlying security at an exercise price during a stated time interval. 0 First, find value at expiration Put Option

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11-22 Value of put option at expiration, E = $100 P E e.g., P = 90P = 100P = 110 Put = E – PPut = 0Put = 0 e.g., Put = 10 in-the-moneyat-the-moneyout-of-money Put Options

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11-23 Case of Put < E – P: Suppose P = 90, E = 100, Put* = 6. Arbitrage: Buy Put-6 Exercise+100 Buy Underlying-90 Arbitrage Profit+4 If P < E, There is Arbitrage unless Put = E – P

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11-24 Case of Put > E – P: Suppose P = 90, E = 100, Put** = 17. Arbitrage: Write Put+17 Exercised-100 Sell Underlying+90 Arbitrage Profit+7

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11-25 Value of put option before expiration, E = $100 P E e.g., P = 90P = 100P = 110 Put > E – PPut > 0Put > 0 e.g., Put = 10 in-the-moneyat-the-moneyout-of-money

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11-26 Price of underlying at expiration 9497100104 Buy put -3 Buy underlying Exercise put Net profit = – Put -3 -3 Net profit = – Put + E – P +3 0 -3 -94 -97 +100 Profits or Losses for Buying a Put Option

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11-27 P exp E Payoff Function: Buy Put E – Put Breakeven – put– put + [E – P exp ] 0 – put + –

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11-28 Profit 0 Loss Buy put Put in-moneyPut out-of-money 100 E Underlying asset at expiration 97 -3 Shortsell Profit Profile for Put Option -PUT -PUT + [E-P]

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11-29 Writing a Put Price of underlying at expiration 9497100104 Write put+3 Sell underlying Put exercised Net profit = + Put +3 +3 Net profit = + Put – E + P +3 +97 -100 0 +3 +94 -100 -3

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11-30 P exp E Payoff Function: Write Put E – put Breakeven + put+ put – [E – P exp ] 0 + put + –

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11-31 Profit 0 Loss Put in-moneyPut out-of-money 100 E Underlying asset at expiration 97 Profit Profile for Writing a Put +3 +PUT+PUT - [E-P]

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11-32 Put-Call Parity C = Put + P – E D 0Expiration Present value =.98 = D = E D = 98 $1 E 100

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11-33 Profit of Put-Call Parity 0Expiration Buy call Cash flows from portfolio Cash flows from call Buy portfolio If cash flows at Expiration are the same for call as for portfolio, then the Time 0 value must be the same.

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11-34 P E Cash flows at expiration from buying call Call00P – E Cash flows at expiration from buying put, buying underlying and borrowing present value of exercise price PutE – P00 Underlying+P+P+P Loan –E –E –E Put-Call Parity

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11-35 Implications of Put-Call Parity C= Put + [P – E D] = Put + [Levered position in underlying] 5= 3 + [100 – 98].

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11-36 ROR on levered Leverage i Lower return from levered Higher return from levered Unlevered Levered ROR unlevered i i = Interest rate

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11-37 C P – E D Call P E If C = Put + P – E D, then C P – E D P – E

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11-38 Arbitrage if C < P – ED Suppose P = 110, E = 100, D =.98. P – E = 10. P – ED = 12.

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11-39 Suppose C* = 11. Arbitrage: Time 0 Buy Call-11 Short Underlying+110 Lend ED-98 Arbitrage Profit+1

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11-40 P E Call00P – E Buy Underlying-P-P-P Receive E+E+E+E NetE – P > 0 E – P = 00 Expiration

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11-41 Call--greater value of call 1.P--greater value of underlying 2.E--lower value of exercise price 3.Greater time to expiration 4.Higher volatility of underlying Factors Affecting the Value of a Call Option

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11-42 Impact of Longer Remaining Life on the Value of a Call Option C P C 2 has a longer life than C 1 P ED is higher for C 2 because D 2 < D 1 C2C2 C1C1 P E P ED 1 P ED 2 E

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11-43 Call Option of Security 1 Prices of underlying90100110 Value of call option 0 0 10 Probability1/31/31/3 Mean value = (0)(1/3) + (0)(1/3) + (10)(1/3) = 3.33 Call Option of Security 2 Prices of underlying80100120 Value of call option 0 0 20 Probability1/31/31/3 Mean value = (0)(1/3) + (0)(1/3) + (20)(1/3) = 6.67 Value of a Call

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11-44 Impact of the Volatility of the Underlying Asset on the Value of a Call Option C P C 2 has greater volatility of underlying asset C2C2 C1C1 P E P ED E

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