Select your own stock and complete the details and steps

Please select a stock or stock index from WIND database or yahoo finance. Suppose that the risk-free rate is rf=2%. You are required to use the following four methods to price a hypothetical at-the-money European option (S=X) that expires in 6 months: 1) Single Period Binomial Tree 2) 20-Period Binomial Tree 3) Black-Scholes Model 4) Monte Carlo Simulation with 100 paths. 1. Please briefly explain the methodology of each aforementioned methods and compare the results from the four models and summarize the results in the table below: ( 40 marks) 2. In the binomial tree case, please study the case when the period extends from 1 to 20. Also compare the result with a Black-Scholes (BS) solution. (20 marks) 3. In the Monte Carlo Simulation, please also study the case when number of path increases from 10 to 100 , as compared to the BS price. (20 marks) 4. Please also discuss the pros and cons of each method. (20 marks)