Problem:
Find the value of American Call option with an exercise price of $150 and a stock price of $145. The stock can go up by 12% and down by 18% in each of the two binomial periods. The risk free rate is 3%. Determine the price of option today using two period binomial option pricing model. Then construct a risk-free hedge of long stock and short option. Also demonstrate that the return is same as the risk-free rate. Explain in detail and specify all calculation and formulas.