In this project, you will develop options strategies in relation to the stock of IBM plc, a multi-national software company. First you will suppose it is 1^st December 2018, and you will form trading strategies based on information available up to 1^st December 2019. In the next question, you will jump forward to 31^st December 2019, and assess the profit from your options strategies, based on the stock price at this later date. In your answer, use European options on non-dividend-paying stock. Assume that the estimated volatility of IBM per annum is calculated as 32.5% (or 0.325). The IBM stock price on 1^st December 2018 is 2365 pence. The 12-month sterling rate for LIBOR on 1^st December 2018 is 1.5% (or 0.015)

a. Suppose you have a long position in the stock on 1^st December 2018. How would you hedge against price declines for a one-year period, using puts and calls options? [30% of the marks]

b. On 1^st January 2020 the price of the IBM stock is 1923 pence. Calculate the payoffs for the strategies you chose in Q1 combined with the long position in the stock. Comment on your results? [20% of the marks]