Question

The current price of a stock is $15. In 6 months, the price will be either $18 or $13. The annual risk-free rate is 6%. Find the price of a call option on the stock that has an strike price of $14 and that expires in 6 months. (Hint: Use daily compounding.) Round your answer to the nearest cent. Assume a 365-day year Please show work in excel

Answer 1

Current stock price, P = 15

Upper limit price, P(U) = 18

Lower Limit price, P(L) = 13

risk free rate = rf = 6%

Strike price, X = 14

ending uppper option payoff, Cu = Max(0,P(U) - X ) = Max(0,18-14) = 4

ending lower option payoff, Cl = Max(0, P(L) - X) = Max(0,13-14) = 0

Share of stock , Ns = (Cu - Cl) / P(U) - P(L) = (4 - 0) / (18-13) = 0.8

Hedge portofolio payoff if stock price is up = Ns * P(U) - Cu = (0.8 * 18) - 4 = 10.4

Hedge portofolio payoff if stock price is down = Ns * P(L) - Cl = (0.8 * 13) - 0 = 10.4

we need to find the present value(PV) of the riskless payoff

it is given by

PV of riskless payoff = (Hedge portofolio payoff) / ( 1 + (rf/365)) ^ 365(t/n)

t = 6 months = 0.5

n= 1

PV of riskless payoff = 10.4 / (1 + (0.06/365)) ^ 365*(0.5/1)

= 10.09

Call option value is given by Vc = Ns * P - PV of riskless payoff

= (0.8 * 15) - 10.09

= 1.91