Question 2 a. Let the stocks of IBM, Google and Amazon. You have a time series of observations for each stock. The sample size is T. Explain in detail, all steps which are necessary to compute the sample variance-covariance matrix of the three stocks. [5 marks] b. Explain in detail how the implied volatility of an option can be computed. [5 marks] c. Prove that the duration of a zero-coupon bond equals its maturity. [5 marks) d. Do you agree with the statement "Let a fixed income portfolio which has a duration equal to zero. This portfolio is subject to no interest rate risk." [5 marks]