Question

1. A stock has a current value of $94 per share. The stock price next period will be an increase of 15% or a decrease of 10% and the one period risk-free rate is 4%.
   1. What is the value of a one period call option on the stock with a strike price of $90? (2 points)
   2. What is the value of a one period put option on the stick with a strike price of $90? (2 points)

Answer 1

Sol :

Stock current Price = $94

Expected to increase over next period = 15%

Expected to increase over next period = 10%

Risk free rate = 4%

CMP as on expiry can be,

94 x 115% =108.1  OR

94 x 90% =84.6

Therefore, probability of both options are:-

p1 = {CMP(1+r)-S2}/(S1-S2)  

where,

CMP = Current CMP

S1 = High CMP as on expiry

S2 = Low CMP as on expiry

p1 = {94(1 + 0.04) - 84.6}/(108.1 - 84.6) = 0.56

p2 = 1-0.56 = 0.44

1) Value of one period call option,

Call Option premium for 108.1 = 108.1 - 90 = 18.1

Call Option premium for 90= 0

Therefore, value of one period call option =(18.1*0.56) /(1+0.04) = $9.75

2) Value of one period put option,

Put Option premium for 108.1 = 0

Call Option premium for 90= 90-84.6 = 5.4

Therefore, value of one period put option = (5.4*0.44) /(1+0.04) = $2.28

Therefore value of a one period call option will be $9.75 and value of a one period put option wil be $2.28