The price of Profile, Inc., stock will be either $82 or $104 at the end of the year. Call options are available with one year to expiration. T-bills currently yield 3 percent. |
a. |
Suppose the current price of the stock is $93. What is the value of the call option if the exercise price is $78 per share? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) |
b. | Suppose the current price of the stock is $93. What is the value of the call option if the exercise price is $88 per share? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) |
a
Upmove (U)= High price/current price=104/93=1.1183 | ||||||
Down move (D)= Low price/current price=82/93=0.8817 | ||||||
Risk neutral probability for up move | ||||||
q = (e^(risk free rate*time)-D)/(U-D) | ||||||
=(e^(0.03*1)-0.8817)/(1.1183-0.8817)=0.62874 | ||||||
Call option payoff at high price (payoff H) | ||||||
=Max(High price-strike price,0) | ||||||
=Max(104-78,0) | ||||||
=Max(26,0) | ||||||
=26 | ||||||
Call option payoff at low price (Payoff L) | ||||||
=Max(Low price-strike price,0) | ||||||
=Max(82-78,0) | ||||||
=Max(4,0) | ||||||
=4 | ||||||
Price of call option = e^(-r*t)*(q*Payoff H+(1-q)*Payoff L) | ||||||
=e^(-0.03*1)*(0.62874*26+(1-0.62874)*4) | ||||||
=17.31 |
b
Upmove (U)= High price/current price=104/93=1.1183 | ||||||
Down move (D)= Low price/current price=82/93=0.8817 | ||||||
Risk neutral probability for up move | ||||||
q = (e^(risk free rate*time)-D)/(U-D) | ||||||
=(e^(0.03*1)-0.8817)/(1.1183-0.8817)=0.62874 | ||||||
Call option payoff at high price (payoff H) | ||||||
=Max(High price-strike price,0) | ||||||
=Max(104-88,0) | ||||||
=Max(16,0) | ||||||
=16 | ||||||
Call option payoff at low price (Payoff L) | ||||||
=Max(Low price-strike price,0) | ||||||
=Max(82-88,0) | ||||||
=Max(-6,0) | ||||||
=0 | ||||||
Price of call option = e^(-r*t)*(q*Payoff H+(1-q)*Payoff L) | ||||||
=e^(-0.03*1)*(0.62874*16+(1-0.62874)*0) | ||||||
=9.76 |
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