The price of a security follows a geometric Brownian motion with drift parameter 0.05 and volatility parameter 0.4. The current price of the security is 100. A new investment that is being marketed costs 10; after 1 year the investment will pay 5 if S(1) < 95, will pay x if S(1) > 110, and will pay 0 otherwise. The nominal interest rate is 6 percent, continuously compounded.

(a) What must be the value of x if this new investment, which can be bought or sold at any level, is not to give rise to an arbitrage?

(b) What is the probability that S(1) < 95?