The price of a non-dividend paying stock “XYZ” follows a geometric Brownian motion with constant expected return of 1% per annum, compounded continuously, and constant volatility of 15% per annum. The time interval in which the stock price changes is 0.01 year.
(a) Write down the expression for the geometric Brownian motion dS of the stock price in this case. [5 marks]
(b) Consider a random function generating the following numbers: Ɛ1= -0.6128 (please, notice the minus sign), Ɛ2=1.3399, Ɛ3=0.8426. Assume a starting stock price of $3. What are the three subsequent stock prices following the starting $3 stock price
