1. Assume the Black-Scholes-Merton framework. Consider a derivative s curity of a stock. You are given: (a) The continuously compounded risk-free interest rate is 0.04. (b) The volatility of the stock is a. (c) The stock does not pay dividends. (d) The derivative security also does not pay dividends. (e) S(t) denotes the time-f price of the stock. (f) The time-t price of the derivative security is [S(t)]-*/6, where & is a positive constant. Find k. 2. The price of a stock is governed by the stochastic differential equation: as() S(() = 0.03d + 0.2d2 (1)- where {Z()) is a standard Brownian motion. Consider the geometric average G = [5(1) x 5(2) x 5(3)]1/3 Find the variance of In[G]. 3. Assume the Black-Scholes-Merton framework. You are given the fol- lowing information for a stock that pays dividends continuously at a rate proportional to its price. (a) The current stock price is 0.25. (b) The stock's volatility is 0.35. (c) The continuously compounded expected rate of stock-price appre- ciation is 157 Calculate the upper limit of the 90% lognormal confidence interval for the price of the stock in 6 months. (Hint: N-1(0.95) = 1.61485)