In: Finance
The price of Swearengen, Inc., stock will be either $65 or $87 at the end of the year. Call options are available with one year to expiration. T-bills currently yield 3 percent. |
a. |
Suppose the current price of the company's stock is $76. What is the value of the call option if the exercise price is $61 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 $76. 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 | $ |
a
Upmove (U)= High price/current price=87/76=1.1447 | ||||||
Down move (D)= Low price/current price=65/76=0.8553 | ||||||
Risk neutral probability for up move | ||||||
q = (e^(risk free rate*time)-D)/(U-D) | ||||||
=(e^(0.03*1)-0.8553)/(1.1447-0.8553)=0.60521 | ||||||
Call option payoff at high price (payoff H) | ||||||
=Max(High price-strike price,0) | ||||||
=Max(87-61,0) | ||||||
=Max(26,0) | ||||||
=26 | ||||||
Call option payoff at low price (Payoff L) | ||||||
=Max(Low price-strike price,0) | ||||||
=Max(65-61,0) | ||||||
=Max(4,0) | ||||||
=4 | ||||||
Price of call option = e^(-r*t)*(q*Payoff H+(1-q)*Payoff L) | ||||||
=e^(-0.03*1)*(0.605207*26+(1-0.605207)*4) | ||||||
=16.8 |
b
Upmove (U)= High price/current price=87/76=1.1447 | ||||||
Down move (D)= Low price/current price=65/76=0.8553 | ||||||
Risk neutral probability for up move | ||||||
q = (e^(risk free rate*time)-D)/(U-D) | ||||||
=(e^(0.03*1)-0.8553)/(1.1447-0.8553)=0.60521 | ||||||
Call option payoff at high price (payoff H) | ||||||
=Max(High price-strike price,0) | ||||||
=Max(87-71,0) | ||||||
=Max(16,0) | ||||||
=16 | ||||||
Call option payoff at low price (Payoff L) | ||||||
=Max(Low price-strike price,0) | ||||||
=Max(65-71,0) | ||||||
=Max(-6,0) | ||||||
=0 | ||||||
Price of call option = e^(-r*t)*(q*Payoff H+(1-q)*Payoff L) | ||||||
=e^(-0.03*1)*(0.605207*16+(1-0.605207)*0) | ||||||
=9.4 |