# Answer to Question #86523 in Financial Math for X

Question #86523

[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?

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?

Expert's answer

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