If the dividend of $1.50 is expected in two months. The European put price is $3.03.
Given:
K=50, r=0.1, σ=0.3, and T=0.25
First step is to find the stock price
S0 = 50−1.50e^ -0.1667×0.1
SO=48.52
Second step is to find di and d2
d1=In(48.52/50)+(0.1+0.09/2)0.25/0.3√0.25
d1 = 0.0414
d2=d1-0.3√0.25
d2 = -0.1086
Third step is to calculate European put price
European put price=-50N(0.1086)e^ -0.1×0.25−48.52N(−0.0414)
European put price=50×0.5432e -^0.1×0.25−48.52×0.4835
European put price=$3.03
Therefore If the dividend of $1.50 is expected in two months. The European put price is $3.03.
The complete question is:
Calculate the price of a three-month European put option on a non-dividend-paying stock with a strike price of $50 when the current stock price is $50, the risk-free interest rate is 10% per annum, and the volatility is 30% per annum. What difference does it make to your calculations in problem 29 if a dividend of $1.50 is expected in two months?
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