Question

The price of Build A Fire Corp. stock will be either $52 or $83 at the end of the year. Call options are available with one year to expiration. T-bills currently yield 5 percent. a. Suppose the current price of the company's stock is $60. What is the value of the call option if the exercise price is $50 per share? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Value of the call option $ b. Suppose the exercise price is $80 and the current price of the company's stock is $60. What is the value of the call option now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Value of the call option $

Answer 1

a

Upmove (U)= High price/current price=83/60=1.3833

Down move (D)= Low price/current price=52/60=0.8667

Risk neutral probability for up move

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

=(e^(0.05*1)-0.8667)/(1.3833-0.8667)=0.3573

Call option payoff at high price (payoff H)

=Max(High price-strike price,0)

=Max(83-50,0)

=Max(33,0)

=33

Call option payoff at low price (Payoff L)

=Max(Low price-strike price,0)

=Max(52-50,0)

=Max(2,0)

=2

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

=e^(-0.05*1)*(0.357299*33+(1-0.357299)*2)

=12.44

b

Upmove (U)= High price/current price=83/60=1.3833

Down move (D)= Low price/current price=52/60=0.8667

Risk neutral probability for up move

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

=(e^(0.05*1)-0.8667)/(1.3833-0.8667)=0.3573

Call option payoff at high price (payoff H)

=Max(High price-strike price,0)

=Max(83-80,0)

=Max(3,0)

=3

Call option payoff at low price (Payoff L)

=Max(Low price-strike price,0)

=Max(52-80,0)

=Max(-28,0)

=0

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

=e^(-0.05*1)*(0.357299*3+(1-0.357299)*0)

=1.02