Assume the Black-Scholes framework. For t 0, let S(t) be the time-t price of a stock.

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Assume the Black-Scholes framework. For t ≥ 0, let S(t) be the time-t price of a stock. You are given:

(i) The stock pays dividends continuously at a rate proportional to its price.

(ii) The 90% lognormal prediction interval for S(2) is (13.1072, 41.9448).

(iii) The 95% lognormal prediction interval for S(4) is (25.7923, 183.1083).

Calculate the width of the 99% lognormal prediction interval for S(6).

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