i have exam coming on financial engineering, and need help asap with this thing. Basically there's a European put option ex dividend. We know that the stock price is $S_t = 85$, the exercise price is $K = 90$, the annual continuously compounded interest rate is $r = 5\%$, End date is within 50 days ($T = t + 50 / 365$) and that probability that the put option will be exercised is $\mathbb{P} \left( K > S_T \right) = 73.76\%$. I have to estimate the put option using Cox-Ross-Rubinstein with 4 periods.

My question is... HOW do I get the volatility? My guess would be from the $\mathbb{P} \left( K > S_T \right) = 73.76\%$, but really don't know how. In the previous part of the problem I estimated it with Black Scholes and got the volatility there, but it doesn't specify that I have the volatility from previous Black Scholes model application.


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