Question

The price of Mega Polls, Inc. stock is $30.80 per share. The forecast is that the stock has a 60% chance of rising to $36.00 or a 40% chance of falling to $27.40. A call option on Mega’s stock has an exercise price of $28 per share. If the Treasury bill rate is 3.0%, what is the likely price of a 1-year call option? (Round your answer to 2 decimal places.)

Answer 1

S0 = 30.80; Su = 36; Sd = 27.40; K = 28; risk-free rate (r) = 3%; time T = 1 year

fu = St - K = Su - K = 36 - 28 = 8

fd = 0 (since call option will be out of the money and won't be exercised)

Now, suppose the portfolio is made up of x number of shares and a bond valued at B.

Then the call option price f = x*S0 + B

Pricing rule:

If St = Su = 36 then portfolio value is Su*x + Be^(rT) = 8 which means 36x + Be^(0.03) = 8 ------ (A)

If St = Sd = 27.40 then portfolio value is Sd*x + Be^(rT) = 0 which means 27.4x + Be^(0.03) = 0 ------- (B)

(A) - (B)

36x - 27.4x = 8

8.60x = 8 so x = 0.9302 shares

Substituting x = 0.9302 in eqn (B), we get B = -27.4*0.9302/e^(0.03) = -24.7351

call option price = x*S0 + B = (0.9302*30.80) - 24.7351 = 3.9161