Question

The price of Chive Corp. stock will be either $67 or $95 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 $75. What is the value of the call option if the exercise price is $65 per share? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.	Suppose the exercise price is $90 and the current price of the company's stock is $75. 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.)

Answer 1

a

Upmove (U)= High price/current price=95/75=1.2667

Down move (D)= Low price/current price=67/75=0.8933

Risk neutral probability for up move

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

=(e^(0.05*1)-0.8933)/(1.2667-0.8933)=0.42305

Call option payoff at high price (payoff H)

=Max(High price-strike price,0)

=Max(95-65,0)

=Max(30,0)

=30

Call option payoff at low price (Payoff L)

=Max(Low price-strike price,0)

=Max(67-65,0)

=Max(2,0)

=2

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

=e^(-0.05*1)*(0.423048*30+(1-0.423048)*2)

=13.17

b

Upmove (U)= High price/current price=95/75=1.2667

Down move (D)= Low price/current price=67/75=0.8933

Risk neutral probability for up move

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

=(e^(0.05*1)-0.8933)/(1.2667-0.8933)=0.42305

Call option payoff at high price (payoff H)

=Max(High price-strike price,0)

=Max(95-90,0)

=Max(5,0)

=5

Call option payoff at low price (Payoff L)

=Max(Low price-strike price,0)

=Max(67-90,0)

=Max(-23,0)

=0

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

=e^(-0.05*1)*(0.423048*5+(1-0.423048)*0)

=2.01