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Unformatted text preview: the payoff is: Payoff = 10(100)($125 – 110) Payoff = $15,000 c. Remembering that each contract is for 100 shares of stock, the cost is: Cost = 10(100)($4.70) Cost = $4,700 The maximum gain on the put option would occur if the stock price goes to $0. We also need to subtract the initial cost, so: Maximum gain = 10(100)($110) – $4,700 Maximum gain = $105,300 If the stock price at expiration is $104, the position will have a profit of: Profit = 10(100)($110 – 104) – $4,700 Profit = $1,300 d. At a stock price of $103 the put is in the money. As the writer, you will make: Net loss = $4,700 – 10(100)($110 – 103) Net loss = –$2,300 At a stock price of $132 the put is out of the money, so the writer will make the initial cost: Net gain = $4,700 At the breakeven, you would recover the initial cost of $4,700, so: $4,700 = 10(100)($110 – ST) ST = $105.30 For terminal stock prices above $105.30, the writer of the put option makes a net profit (ignoring transaction costs and the effects of the time value of money). 4. a. The value of the call is the stock price minus the present value of the exercise price, so: C0 = $70 – 60/1.06 C0 = $13.40 440 b. Using the equation presented in the text to prevent arbitrage, we find the value of the call is: $70 = [($85 – 65)/($85 – 80)]C0 + $65/1.06 C0 = $2.17 5. a. The value of the call is the stock price minus the present value of the exercise price, so: C0 = $60 – $35/1.05 C0 = $26.67 b. Using the equation presented in the text to prevent arbitrage, we find the value of the call is: $60 = 2C0 + $50/1.05 C0 = $6.19 6. Using putcall parity and solving for the put price, we get: $47 + P = $45e–(.026)(3/12) + $3.80 P = $1.51 7. Using putcall parity and solving for the call price we get: $57 + $4.89 = $60e–(.036)(.5) + C C = $2.96 8. Using putcall parity and solving for the stock price we get: S + $3.15 = $85e–(.048)(3/12) + $6.12 S = $86.96 9. Using putcall parity, we can solve for the riskfree rate as follows: $47.30 + $2.65 = $45e–R(2/12) + $5.32 $44.63 = $45e–R(2/12) 0.9917 = e–R(2/12) ln(0.9917) = ln(e–R(2/12)) –0.0083 = –R(2/12) Rf = 4.95% 10. Using the BlackScholes option pricing model to find the price of the call option, we find: d1 = [ln($46/$50) + (.06 + .542/2) × (3/12)] / (.54 × d2 = –.1183 – (.54 × N(d1) = .4529 N(d2) = .3489 3 / 12 ) = –.1183 3 / 12 ) = –.3883 441 Putting these values into the BlackScholes model, we find the call price is: C = $46(.4529) – ($50e–.06(.25))(.3489) = $3.65 Using putcall parity, the put price is: Put = $50e–.06(.25) + 3.65 – 46 = $6.90 11. Using the BlackScholes option pricing model to find the price of the call option, we find: d1 = [ln($93/$90) + (.04 + .622/2) × (8/12)] / (.62 × d2 = .3706 – (.62 × N(d1) = .6445 N(d2) = .4460 Putting these values into the BlackScholes model, we find the call price is: C = $93(.6445) – ($90e–.04(8/12))(.4460) = $20.85 Using putcall parity, the put price is: Put = $90e–.04(8/12) + 20.85 – 93 = $15.48 12. The delta of a call option is N(d1), so: d1 = [ln($74/$70) + (.05 + .562/2) × .75] / (.56 × N(d1) = .6680 For a call option the delta is .6680. For a put option, the delta is: Put delta = .6680 – 1 = –.3320 The delta tells us the change in the price of an option for a $1 change in the price of the underlying asset. 13. Using the BlackScholes option pricing model, with a ‘stock’ price of $1,900,000 and an exercise price of $2,100,000, the price you should receive is: d1 = [ln($1,900,000/$2,100,000) + (.05 + .252/2) × (12/12)] / (.25 × d2 = –.0753 – (.25 × N(d1) = .4700 N(d2) = .3725 8 / 12 ) = .3706 8 / 12 ) = –.1357 .75 ) = .4344 12 / 12 ) = –.0753 12 / 12 ) = –.3253 442 Putting these values into the BlackScholes model, we find the call price is: C = $1,900,000(.4700) – ($2,100,000e–.05(1))(.3725) = $148,923.92 14. Using the call price we found in the previous problem and putcall parity, you would need to pay: Put = $2,100,000e–.05(1) + 148,923.92 – 1,900,000 = $246,505.71 You would have to pay $246,505.71 in order to guarantee the right to sell the land for $2,100,000. 15. Using the BlackScholes option pricing model to find the price of the call option, we find: d1 = [ln($74/$80) + (.06 + .532/2) × (6/12)] / (.53 × d2 = .0594 – (.53 × N(d1) = .5237 N(d2) = .3762 Putting these values into the BlackScholes model, we find the call price is: C = $74(.5237) – ($80e–.06(.50))(.3762) = $9.54 Using putcall parity, we find the put price is: Put = $80e–.06(.50) + 9.54 – 74 = $13.18 a. The intrinsic value of each option is: Call intrinsic value = Max[S – E, 0] = $0 Put intrinsic value = Max[E – S, 0] = $6 b. Option value consists of time value and intrinsic value, so: Call option value = Intrinsic value + Time value $9.54 = $0 + TV TV = $9.54 Put option value = Intrinsic value + Time value $13.18 = $6 + TV TV = $7.18 c. The time premium (theta) is more important for a call option than a put option...
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This note was uploaded on 07/10/2010 for the course FIN 6301 taught by Professor Eshmalwi during the Spring '10 term at University of TexasTyler.
 Spring '10
 eshmalwi
 Finance, Corporate Finance

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