THIS IS THE COMPLETE QUESTION.

Assume we are using the Black Scholes model where the risk free investment earns a continuously compounded rate r and the stock price satisfies the stochastic differential equation dS(t) = S(t)dt + S(t)dBt (1) 1. What are the prices of the asset or nothing put and cash or nothing put? Thes options pay when S(T) < K. 2. Use risk neutral valuation to find the price of a derivative security that pays log(S(T)). 3. Use risk neutral valuation to find the price of a security that pays S(T)². Note: (e^x)² = e^2x