We are interested in pricing a 1-year put option on cisco with a strike price of K=100. Currently CISCO is trading at 80 and the risk free rate is 5% per annum. In addition we assume that (i) CISCO will not pay any dividend and (ii) there are no other derivatives that are trading including other call or put options.

a) Suppose that we follow a Binomial model and CISCO may either appreciate by 50% or depreciate by 25%.

What should be the price of the option based on replication?

What should be the price of the option based on risk neutral pricing?

b) In this part we no longer assume a Binomial structure and future stock price can take arbitrary non-negative values. For each of the following possible prices for the put option determine whether it admits an arbitrage strategy.: (i) 100 (ii) 60 (iii) 10

In case there is an arbitrage, describe explicitly such strategy and calculate arbitrage profit today as well as payoff diagram in 1 year; in case there is not you are not required to prove it. 3

c) Suppose now that there is also a call option with a strike of k=90 that costs $10. For each of the following possible prices for the put option determine whether it admits an opportunity strategy: (i) 20 (ii) 30

Again as in part b), in case there is an arbitrage, describe explicitly such strategy and calculate arbitrage profit today as well as payoff diagram in 1 year; in case there is not you are not required to prove it.