We must price a 1 year put option on cisco with a strike price of K=100. At the moment CISCO trades at 80 and the risk free rate is 5% pa. Also it is assumed CISCO does not pay a dividend and there are no other derivatives trading including other call or put options

a. Suppose we follow a binomial model and CISCO either appreciates by 50% or depreciates by 25%.

What should the price of the option be using replication?

What should the price of the option be based using neutral pricing?

b. Binomial structure is now not assumed and future stock prices can take arbitrary non-negative values. For each price for the put option work out if it admits arbitrage strategy i. 100 ii. 60 iii. 10

In the case of arbitrage, describe such strategy and calculate arbitrage profit today and payoff diagram in 1 year; in the case there is not, it is not necessary to prove