Consider an option on a non-dividend-paying stock when the stock price is $30, the exercise price is $29, the risk-free interest rate is 5% per annum, the volatility is 25% per annum, and the time to maturity is four months. Assume that the stock is due to go ex-dividend in 1.5 months. The expected dividend is 50 cents. Using the Black-Scholes-Merton model, what is the price of the option if it is a European put?
Stock price S0 = $30
Exercise price K = $29
Interest rate r = .05
T = 4/12
The present value of the dividend must be substracted form the stock price
30-0.5e-0.125*0.05 = 29.5031
N(-d2) = 0.3795, N(-d2) =0.4355
We get 0.3795 by using NORMSDIST Function in Excel
=N(-3068) = 0.6205 Same method for N(-d2)
The Price of option when it is European Put is
29e-0.05*4/12 * 0.4355 - 29.5031 * .3795 = $1.22
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