Choose one stock from the New  York stock market which has calls and puts available. Extract  the price change for each 3 month period over the last 12 months. Find the current yield on 12 month US treasury bills and use as the risk free rate. 

(a) Assume price changes for each of the last four 3-month periods is repeated in the next 12 months. Assume an expected dividend payment at the start of the 4th period of 5%. Use a four period (each three months) binomial model to estimate the theoretical current fair price of both a European call and a European put.

(b) Use the Black-Scholes Model to estimate the theoretical current fair price of both a European call and a European put on your stock, with the strike price matching an existing call and put. Use the monthly price changes for your stock for the last 12 months to estimate the mean, standard deviation. Assume no dividends. Compare this to the market price of the call and put. Explain why differences in price between the theoretical prices calculated and the market price can occur.

(c) If you expect the price of your stock to have a 70% of rising by 20% and a 30% chance of falling by 20% over the next 12 months, explain how you could use an advanced option spread strategy to leverage your gains from an increase in the stock price whilst minimising the losses from a decrease.

(d) Assume you owned an initial 1,000 shares. How much  would you gain from your spread strategy if the price actually rose by 15% after 12 months? How much would you lose if the price fell by 20%? Use the current market price of calls or puts at your chosen strike prices.

(e) Assume you had implemented your strategy 12 months ago. Graph your month end profit/ loss for each of the last 12 months. What is the % return on your initial investment? What is the std dev of your monthly profit/loss?

(f) Discuss the advantages and disadvantages of your spread strategy.