(a) If this investment is not to give rise to an arbitrage, what is C?

(b) What is the probability the investment makes money for its buyer?

The price of a traded security follows a geometric Brownian motion with drift 0.06 and volatility 0.4. Its current price is 40. A brokerage firm is offering, at cost C, an investment that will pay 100 at the end of 1 year either if the price of the security at 6 months is at least 42 or if the price of the security at 1 year is at least 5 percent above its price at 6 months. That is, the payoff occurs if either S(0.5) ≥ 42 or S(1) > 1.05 S(0.5). The continuously compounded interest rate is 0.06.

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