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[10 points] The financial wizard Joe Getrichfast offers you the following deal for a fee of $100: buy 100 shares of a stock that will rise at least 20% by
three weeks from now with 66% probability.
Let S(0) be the initial price of a stock. Let S(n) be the price of the same stock
at the end of the nth week, n ≥ 1. According to Joe Getrichfast the evolution of
these prices follows the rule that S(n+1)
S(n)
are independent log-normal variables with
lognormal parameters µ = 0.135252, σ = 0.3 for n ≥ 0.
(a) Verify the wizard’s claim that the stock price will rise at least 20% with 66%
probability.
(b) Calculate the net gain of the investor in the event that the stock price rises
20%. The transaction cost of trading 100 shares is $8 and according to financial
wizard the initial price of the stock is S(0) = $52.
(c) Being a cautious investor you want to evaluate the downside. What is the
probability that your investment will be worth less than half of its original value at
the end of the third week?

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