(4) Consider a trinomial tree model with risk-free interest rate r = 0.15 and a stock with initial value S (0) and independent one-step returns K(n) given by 0.75 in scenario S (0) = 100, K(n) = 0.25 in scenario -0.75 in scenario 3 (a) What are the arbitrage-free prices at time 0 of i. a put option with strike price 125 and expiration time 1? ii. a call option with strike price 200 and expiration time 2? (b) What are the arbitrage-free prices at time 1 in the scenario S (1) = 125 of a call option with strike price 200 and expiration time 2? (c) Assume that there is an additional stock with initial value S(0) and inde- pendent one-step returns K(n) given by 0.75 in scenario S (0) = 100, K(n) 0 in scenario -0.5 in scenario 3 What are the arbitrage-free prices at time 0 of i. a put option on the first stock with strike 125 and expiration time 1? ii. a call option on the first stock with strike 200 and expiration time 2? iii. a payoff (min{S(1), S(1)} 100)+at time 1? (4) Consider a trinomial tree model with risk-free interest rate r = 0.15 and a stock with initial value S (0) and independent one-step returns K(n) given by 0.75 in scenario S (0) = 100, K(n) = 0.25 in scenario -0.75 in scenario 3 (a) What are the arbitrage-free prices at time 0 of i. a put option with strike price 125 and expiration time 1? ii. a call option with strike price 200 and expiration time 2? (b) What are the arbitrage-free prices at time 1 in the scenario S (1) = 125 of a call option with strike price 200 and expiration time 2? (c) Assume that there is an additional stock with initial value S(0) and inde- pendent one-step returns K(n) given by 0.75 in scenario S (0) = 100, K(n) 0 in scenario -0.5 in scenario 3 What are the arbitrage-free prices at time 0 of i. a put option on the first stock with strike 125 and expiration time 1? ii. a call option on the first stock with strike 200 and expiration time 2? iii. a payoff (min{S(1), S(1)} 100)+at time 1