Question

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.)

Answer 1

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