In a one-period model with parameters S$_0$= 4, u= 2,d= 1/2, and r= 1/4, consider an American put option with strike priceK. Determine the values of K for which it is optimal to exercise the option at time 0.the problem
(additionally I calculated p and q, both are 1/2)
It's an american put, so max{1,4/5(.5[0+3])} are the exercising options, and we want to say that k is variable and choose what is the needed k for a definitive exercising time at time 1.
Since the alternative investment is sticking the money in the bank to accumulate with a rate of 1.25. So, I set the market rate equal to the value of the portfolio at time 1 with the strike price as varying and I get I set 1.25$>=$4/5(.5[k-2]+.5[0]) means we get k$<=$5.125 thus we exercise at time 0 for any k$<=$5.125.
Is this the correct reasoning?