4.(15%) S.(UU)=81 S.(U)=54 So=36 S:(UD)=s:(DU)=36 AS (D)=24 S(DD)=16 The above graph presents a two-period binomial model, where the per period risk free interest rate rf is 1/9 (11.111111%; NOT r.). The strike price of European put option P which will expire at time 2 is 40 (i.e., X-40). For any given scenario (UU, UD, DU or DD), put option payoff at time 2, P2, is max(0, X-S). (a) (3%) Calculate the up parameter u and the risk-neutral probability p for the up move (risk-free savings account as numeraire) (b) (3%) Calculate stock-measure (using stock price as numeraire) for the up move. (c)(3%) Under stock-measure (using stock price as numeraire), calculate E;[P/S:](U) at time 1. (d) (39) Under stock-measure (using stock price as numeraire), calculate Ex[P/S.)(D) at time I. (e) (3%) Find P. (European put option price) using Eo[P/S:]=P/S.. 4.(15%) S.(UU)=81 S.(U)=54 So=36 S:(UD)=s:(DU)=36 AS (D)=24 S(DD)=16 The above graph presents a two-period binomial model, where the per period risk free interest rate rf is 1/9 (11.111111%; NOT r.). The strike price of European put option P which will expire at time 2 is 40 (i.e., X-40). For any given scenario (UU, UD, DU or DD), put option payoff at time 2, P2, is max(0, X-S). (a) (3%) Calculate the up parameter u and the risk-neutral probability p for the up move (risk-free savings account as numeraire) (b) (3%) Calculate stock-measure (using stock price as numeraire) for the up move. (c)(3%) Under stock-measure (using stock price as numeraire), calculate E;[P/S:](U) at time 1. (d) (39) Under stock-measure (using stock price as numeraire), calculate Ex[P/S.)(D) at time I. (e) (3%) Find P. (European put option price) using Eo[P/S:]=P/S