Q2 (Option Prices and Finite-Difference Methods) (25 Marks) 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)+] Answer the following questions: 1) Work out EQ[1ST>K] (e.g., prob(ST>K)) and EQ[1ST=K]( e.g., prob(1ST=K)), where 1(.) is an indicator function, equal to 1 if ST=K and 0 otherwise. (10 marks) 2) Apply the finite-difference methods to approximate EQ[1ST>K] and EQ[1ST=K]. Outline the key steps in the algorithm. (15 marks)