(25 Points) Replicate the payoff of a one-year down-and-out European put with a strike of 80 and a barrier of 60 . The current stock price is 100 . The stock pays no dividends, and the riskless rate is zero. Assume BSM and an implied volatility of 20%. (a) Use three vanilla European options to match the payoff of the down-and-out put a) at expiration when the barrier has not been hit, b) six months prior to expiration, at barrier and c) today, at barrier. (b) What is the value of replication portfolio? (25 Points) Replicate the payoff of a one-year down-and-out European put with a strike of 80 and a barrier of 60 . The current stock price is 100 . The stock pays no dividends, and the riskless rate is zero. Assume BSM and an implied volatility of 20%. (a) Use three vanilla European options to match the payoff of the down-and-out put a) at expiration when the barrier has not been hit, b) six months prior to expiration, at barrier and c) today, at barrier. (b) What is the value of replication portfolio