Assume the Black-Scholes framework. For a 3-month at-the-money European put option on a stock, you are given:

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Assume the Black-Scholes framework. For a 3-month at-the-money European put option on a stock, you are given:

(i) The stock is currently selling for 50.

(ii) The stock will pay a single dividend of 1.5 in two months.

(iii)  Var[ln FPt,0.25(S)] = 0.09t, for 0 ≤ t ≤ 0.25.

(iv) The continuously compounded risk-free interest rate is 10%.

The stock price when the put option expires is 45.

Calculate the 3-month profit on the put option.

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