Question

The price of Swearengen, Inc., stock will be either $73 or $95 at the end of the year. Call options are available with one year to expiration. T-bills currently yield 4 percent. a. Suppose the current price of the company's stock is $84. What is the value of the call option if the exercise price is $69 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 $84. What is the value of the call option if the exercise price is $79 per share? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Call value $ HintsReferenceseBook & Resources Hint #1

Answer 1

a

Upmove (U)= High price/current price=95/84=1.131

Down move (D)= Low price/current price=73/84=0.869

Risk neutral probability for up move

q = (e^(risk free rate*time)-D)/(U-D)

=(e^(0.04*1)-0.869)/(1.131-0.869)=0.65582

Call option payoff at high price (payoff H)

=Max(High price-strike price,0)

=Max(95-69,0)

=Max(26,0)

=26

Call option payoff at low price (Payoff L)

=Max(Low price-strike price,0)

=Max(73-69,0)

=Max(4,0)

=4

Price of call option = e^(-r*t)*(q*Payoff H+(1-q)*Payoff L)

=e^(-0.04*1)*(0.655823*26+(1-0.655823)*4)

=17.71

b

Upmove (U)= High price/current price=95/84=1.131

Down move (D)= Low price/current price=73/84=0.869

Risk neutral probability for up move

q = (e^(risk free rate*time)-D)/(U-D)

=(e^(0.04*1)-0.869)/(1.131-0.869)=0.65582

Call option payoff at high price (payoff H)

=Max(High price-strike price,0)

=Max(95-79,0)

=Max(16,0)

=16

Call option payoff at low price (Payoff L)

=Max(Low price-strike price,0)

=Max(73-79,0)

=Max(-6,0)

=0

Price of call option = e^(-r*t)*(q*Payoff H+(1-q)*Payoff L)

=e^(-0.04*1)*(0.655823*16+(1-0.655823)*0)

=10.08