Question

Assuming current stock price of ABC Company is $100. Over each of the next two six-month periods, the price is expected to go up by 10% or down by 10% during each six-month period. The risk-free interest rate is 8% per annum with annual compounding. Required:

a. Calculate the option premium for a one-year European call option with an exercise price of $80. Show your calculation steps.

b. Using the option premium calculated in Part a of Question 9, estimate the premium of a one-year European put option that has the same exercise price and the same expiration date.

Answer 1

We use replicating portfolio approach to find call option premium

S= 100

Su= 100+10% = 110

SD= 100-10% = 90

Strike price is 80

Risk free rate is 8% for 6 months is 4%

Cu(value of call at su) = 110-80 = 30

Cd(value of call at sd) = 90-80 = 10

Value of call = delta (s)-B

Where Delta is no of shares to be bought to replicate portfolio

B is amount to be borrowed

Delta= (cu-cd)/(su-sd) = (30-10)/(110-90)

= 1

B=(cusd-cdsu)/(su-sd)(1+r)

= (30×90-10×110)/((110-90)(1.04))

= 76.923

Value of call is = 1(100)-76.923 = 23.077

Premium on call option = 23.077

B) we will value put using put call parity

We have

C+pv(x) = p + s

Where x is strike price

23.077 + 80/(1.04) = p + 100

P= 100-100 = 0

So value of put is 0 from put call parity