Question

The price of Swearengen, Inc., stock will be either $75 or $97 at the end of the year. Call options are available with one year to expiration. T-bills currently yield 7 percent.

  

a.	Suppose the current price of the company's stock is $86. What is the value of the call option if the exercise price is $71 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 $86. What is the value of the call option if the exercise price is $81 per share? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Call value

$

Answer 1

a

Upmove (U)= High price/current price=97/86=1.1279

Down move (D)= Low price/current price=75/86=0.8721

Risk neutral probability for up move

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

=(e^(0.07*1)-0.8721)/(1.1279-0.8721)=0.78344

Call option payoff at high price (payoff H)

=Max(High price-strike price,0)

=Max(97-71,0)

=Max(26,0)

=26

Call option payoff at low price (Payoff L)

=Max(Low price-strike price,0)

=Max(75-71,0)

=Max(4,0)

=4

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

=e^(-0.07*1)*(0.783441*26+(1-0.783441)*4)

=19.8

b

Upmove (U)= High price/current price=97/86=1.1279

Down move (D)= Low price/current price=75/86=0.8721

Risk neutral probability for up move

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

=(e^(0.07*1)-0.8721)/(1.1279-0.8721)=0.78344

Call option payoff at high price (payoff H)

=Max(High price-strike price,0)

=Max(97-81,0)

=Max(16,0)

=16

Call option payoff at low price (Payoff L)

=Max(Low price-strike price,0)

=Max(75-81,0)

=Max(-6,0)

=0

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

=e^(-0.07*1)*(0.783441*16+(1-0.783441)*0)

=11.69