4. The opening values of Amazon's shares (AMZN) recorded at the beginning of each month from February 2020 to January 2021 are: Feb $2,010.60|| Jun $2,448.00 || Oct $3,208.00 Mar $1,906.49 Jul $2,757.99 Nov $3,061.74 Apr $1,932.97 Aug $3,180.51 Dec $3,188.50 May $2,336.80 Sep $3,489.58 Jan $3,270.00 (i) Compute their monthly logarithmic returns. Hence based on such histor- ical data, estimate the monthly drift and volatility of the AMZN stock. (ii) Using the data computed in (i), model the future AMZN share values with the N-step log-normal random walk model S(t) = S(0) elt+aWN(t) (a) Define what are , o, and WN(t) in the above N-step log-normal random walk model. (b) Compute the future values in 2 months of the AMZN stock using first a 2-step model and then a 3-step model. (c) Assume that the risk-free asset's interest rate compounded continu- ously is r = 1% per year. Using the future AMZN stock values ob- tained with the 2-step model, find the premium and the values at each time step of a European put option having strike price X = $3,300, expiry time in 2 months and whose underlying asset is the AMZN stock. (d) Compute the expected value of the AMZN stock values at time t > 0 for the log-normal random walk with N steps and in the limit N . You may use the resulte-2/2dz = 2.