4. Suppose the current price of a stock is $100, and that interest can be com- pounded continuously at a rate of 5%. (a) What type of assumptions about the stock price would allow you to con- clude that the logarithm of the price evolves according to a Brownian motion with drift? You do not need to present a rigorous proof that these assumptions lead to the desired conclusion, but you should provide some explanation. (b) Assuming the assumption from 4(a) above holds with variance parameter o = 1.5, what is the cost of an option to buy the stock at time 10 for 120 per unit