. Consider the setting of the in-class example. A stock price is currently $100. It is known that by the end of the next two months it will be either $120 or $80. The European call option on the stock with the strike price $110 expires in 2 months. The risk-free annual interest rate compounded continuously is 10%.

By no-arbitrage arguments (see your class notes) we have found that the fair price of the option is $5.33.

Consider the following cases:

1. the actual market price of the call option is $6
2. the actual market price of the call option is $5.10

For each of the above cases show that there is an arbitrage opportunity on the market and describe a possible arbitrage strategy in detail.

Hint. The risk-free portfolio value at maturity is $20. The present value of the risk-free portfolio (discounted at the risk-free rate 10%) is $19.669. Compare the set-up cost of the hedging portfolio in each of the cases (a) and (b) with the present value of the risk-free portfolio and build your argument on that comparison.