1) Assume that in the continuous setup, St follows a Geometric Brownian process under the probability measure Q: StdSt=rdt+dWt where dWt presents a Brownian motion process. Show that the first two moments (e.g., mean and variance) of the stock price over the time interval of are given by: E[StSt+]=erandVar[StSt+]=e2r(e21)(10marks) 2) Suppose that the annual risk-free rate (r) is continuously compounded. Consider the time-zero pricing formula for a European call with strike price K and maturity T : c0=erTEQ[(STK)+] Work out prob( Sr>K) and further apply the finite-difference methods to approximate prob( ST>K). Outline the key steps in the algorithm. (15 marks)