Problem 4. A former UConn student is working for a large investment bank. She has invented a new derivative security on Amazon shares. The security expires in one year and pays at maturity the average of the monthly prices of the shares. In other words, at time T = 1 year the security will pay its holder the amount of money 1 S 12 12 () where S () is the Amazon share price at the end of ith month. Compute V, the arbitrage-free price of the derivative security assuming that the current share price S(0) = $100 and the monthly annual interest rate r(12) = 12% (interest per month is r(12)/12 = 1%). Assume that the shares of Amazon do not pay dividends and that one can buy a fraction of a share