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St is the price of a non-dividend-paying stock at time t. St follows a lognormal model. You are given (i) S0 = 45. (ii) The
St is the price of a non-dividend-paying stock at time t. St follows a lognormal model. You are given
(i) S0 = 45.
(ii) The continuously compounded expected rate of return is 0.15.
(iii) The volatility is 0.2.
Asking:
(a) The probability that the stock price is less than 40 at time t is 0.10. Determine all possible values for t. [You may use 1 (0.10) = 1.28155.]
(b) Let pt be the probability that St is less than 40. Determine the value of t for which pt is maximized overall positive t
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