Question

9. You are given the following information for a non-dividend paying stock: 1) the current stock price is 0.25; 2) the stock’s volatility is 0.35; 3) the continuously compounded expected rate of return from the stock is 15%. Calculate the upper limit K such that in 6 months (i.e. T = 0.5) P[S(T) ≤ K] = 90%.

Answer 1

Using the concept of Black Scholes Merton model, we find the upper limit of K

Given - P[S(T) ≤ K] = 90% this implies that the z score for this is 1.645

K = S*e^(r - sigma^2/2)*t +/- sigma*T^0.5*1.645

S = 0.25, r = 0.15, sigma = 0.35, T = 0.5

Lets calculate -

Hence, upper limit = 0.39265