(a) 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. 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] What is the replicating portfolio of the European call option at the initial node i.e. today? [6 marks] (111) How does the price of the call option change if it's an American option? [3 marks) 11) b) (c) Using the parameters of the Black-Scholes options pricing model explain how increases in each parameter, holding all other parameters constant, affects the price of a European call option on a non-dividend paying stock. [10 marks] You are a researcher for an investment bank and are trying to determine how stock prices react to dividend announcements. Describe in detail how you would conduct an event study to investigate whether the market reacts to announcements of dividend changes in a timely and accurate fashion. [8 marks]