1. Stock ABC has a current price of 80 and in each of the next 3 month periods will either increase by 50% or fall by 10%. Stock ABC will not pay any dividends over the next year and the risk-free rate is 2% for each 3 month period.

   1. (i) Use the risk-neutral method to calculate the no arbitrage price of a European call option on Stock ABC with 6 months to maturity that has an exercise price of 85. [6 marks]

   2. (ii) What is the replicating portfolio of the European call option at the initial node i.e. today? [6 marks]

   3. (iii) How does the price of the call option change if its an American option? [3 marks]