1. The stock price of a company is currently $50 and the price can either increase by 10% or decrease by 5 % in each of the next two years. There is a two-year European call option on the stock with a strike price of $54. Calculate the price of the option assuming a risk-free interest rate of 4% and plot the binomial tree with the estimated final and intermediate option prices at each node.

2. Using the data and results from Question 1: a) What is the volatility of the stock given the information about price increase / decrease in each of the next two years? b) Is the early exercise of an American call option optimal given the same data?