Question

The price of Build A Fire Corp. stock will be either $61 or $86 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 $70. What is the value of the call option if the exercise price is $60 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 $70. 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=86/70=1.2286

Down move (D)= Low price/current price=61/70=0.8714

Risk neutral probability for up move

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

=(e^(0.04*1)-0.8714)/(1.2286-0.8714)=0.47427

Call option payoff at high price (payoff H)

=Max(High price-strike price,0)

=Max(86-60,0)

=Max(26,0)

=26

Call option payoff at low price (Payoff L)

=Max(Low price-strike price,0)

=Max(61-60,0)

=Max(1,0)

=1

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

=e^(-0.04*1)*(0.47427*26+(1-0.47427)*1)

=12.35

b

Upmove (U)= High price/current price=86/70=1.2286

Down move (D)= Low price/current price=61/70=0.8714

Risk neutral probability for up move

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

=(e^(0.04*1)-0.8714)/(1.2286-0.8714)=0.47427

Call option payoff at high price (payoff H)

=Max(High price-strike price,0)

=Max(86-80,0)

=Max(6,0)

=6

Call option payoff at low price (Payoff L)

=Max(Low price-strike price,0)

=Max(61-80,0)

=Max(-19,0)

=0

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

=e^(-0.04*1)*(0.47427*6+(1-0.47427)*0)

=2.73