The price of a certain stock follows a geometric Brownian motion with an expected rate of return of 10% per annum and a volatility of 20% per annum. Suppose that an initial price is $80. (a) Using MATLAB, generate and plot three one-year sample paths for the stock price movement. (b) Clearly write down the probability density function of the stock price in 6 months, and then plot it in MATLAB. (c) Find an interval which there is a 95% probability that the stock price in 6 months will lie. The price of a certain stock follows a geometric Brownian motion with an expected rate of return of 10% per annum and a volatility of 20% per annum. Suppose that an initial price is $80. (a) Using MATLAB, generate and plot three one-year sample paths for the stock price movement. (b) Clearly write down the probability density function of the stock price in 6 months, and then plot it in MATLAB. (c) Find an interval which there is a 95% probability that the stock price in 6 months will lie