Question

iA stock price is currently selling at sh. 50. It is known that at the end of six months it will be either sh. 45 or sh. 55. The risk-free rate is 10% per annum with continuous compounding. What is the value of a six-month European call option with a strike price of sh. 50?

Answer 1

If a stock price is currently selling at sh. 50, at the end of six months it will be either sh. 45 or sh. 55 and the risk-free rate is 10% per annum with continuous compounding, then we have u = 1.1, d = 0.9, r = 0.10, T = 0.5, and K = 50.
So, p = (e^(0.10)(0.5) − 0.9)/(1.1 - 0.9) = 0.7564 and 1 − p = 0.2436.
The value of the put is therefore f = e^-(0.10)(0.5)*[0.7564*0 + 0.2436*5] = $1.16