1. An American call option on a non-dividend-paying stock is currently trading in CBOT market. The price of the underlying stock is $36, the option strike price is $30, and the option expiration date is in three months. The risk-free interest rate is 8%.

   a) Calculate upper and lower bounds for the price of this American call option.

   b)Explain the arbitrage opportunities presented to an arbitrageur when this American call option is trading at $37 and when it is trading at $4. Calculate the risk-free profits that can be earned by an arbitrageur in both cases. (Note: calculate the risk-free profit also for both scenarios at maturity i.e. when ST is greater than $30 and when ST is lower than $30)