The price of Swearengen, Inc., stock will be either $75 or $97 at the end of the year. Call options are available with one year to expiration. T-bills currently yield 7 percent. |
a. |
Suppose the current price of the company's stock is $86. What is the value of the call option if the exercise price is $71 per share? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) |
Call value | $ |
b. |
Suppose the current price of the company's stock is $86. What is the value of the call option if the exercise price is $81 per share? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) |
Call value | $ |
a
Upmove (U)= High price/current price=97/86=1.1279 | ||||||
Down move (D)= Low price/current price=75/86=0.8721 | ||||||
Risk neutral probability for up move | ||||||
q = (e^(risk free rate*time)-D)/(U-D) | ||||||
=(e^(0.07*1)-0.8721)/(1.1279-0.8721)=0.78344 | ||||||
Call option payoff at high price (payoff H) | ||||||
=Max(High price-strike price,0) | ||||||
=Max(97-71,0) | ||||||
=Max(26,0) | ||||||
=26 | ||||||
Call option payoff at low price (Payoff L) | ||||||
=Max(Low price-strike price,0) | ||||||
=Max(75-71,0) | ||||||
=Max(4,0) | ||||||
=4 | ||||||
Price of call option = e^(-r*t)*(q*Payoff H+(1-q)*Payoff L) | ||||||
=e^(-0.07*1)*(0.783441*26+(1-0.783441)*4) | ||||||
=19.8 |
b
Upmove (U)= High price/current price=97/86=1.1279 | ||||||
Down move (D)= Low price/current price=75/86=0.8721 | ||||||
Risk neutral probability for up move | ||||||
q = (e^(risk free rate*time)-D)/(U-D) | ||||||
=(e^(0.07*1)-0.8721)/(1.1279-0.8721)=0.78344 | ||||||
Call option payoff at high price (payoff H) | ||||||
=Max(High price-strike price,0) | ||||||
=Max(97-81,0) | ||||||
=Max(16,0) | ||||||
=16 | ||||||
Call option payoff at low price (Payoff L) | ||||||
=Max(Low price-strike price,0) | ||||||
=Max(75-81,0) | ||||||
=Max(-6,0) | ||||||
=0 | ||||||
Price of call option = e^(-r*t)*(q*Payoff H+(1-q)*Payoff L) | ||||||
=e^(-0.07*1)*(0.783441*16+(1-0.783441)*0) | ||||||
=11.69 |
The price of Swearengen, Inc., stock will be either $75 or $97 at the end of...
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