Question

The price of Ervin Corp. stock will be either $54 or $87 at the end of the year. Call options are available with one year to expiration. T-bills currently yield 2 percent.

     

a.	Suppose the current price of the stock is $63. 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.)
b.	Suppose the exercise price is $80 and the stock price is $63. 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).

c+ = Max(0,S+-X)

Where, S+ is the stock price when up move occurs

c+ is the call option value when the stock goes upwards

X is the exercise price

c+ = Max(0,87-50) = $37

c- = Max(0,S--X)

Where, S- is the stock when down move occurs

c- is the call option when the stock goes downwards

c- = Max(0,54-50) = $4

Hedge ratio, h = (c+-c-)/(S+-S-)

= (37-4)/(87-54)

= 33/33 = 1

Present value factor = 1/(1+r) = 1/(1+0.02) = 0.980392

The call option value is calculated using no-arbitrage approach below

c = hS + PV(-hS- + c-)

Where, S is the current stock price and c is the call option value now

c = 1*63 + 0.980392*(-1*54 + 4)

= 63 +(-49.0196)

= $13.98

b).

c+ = Max(0,87-80) = $7

c- = Max(0,54-80) = 0

h = (7-0)/(87-54) = 0.21212

c = 0.21212*63 + 0.980392*(-0.21212*54+0)

= $2.13