Your services have been retained as an investment advisor to Omega In vestments Ltd, a Nairobi based company that heavily invests in stocks. Omega invests in the stock of Alpha Telecommunications Ltd currently trading at KES 100. Based on your long term capital markets expec tations you strongly believe that the stock market will perform well in the foreseeable future. This strong performance of the stock market to gether with Alpha's favourable fundamentals has made you to assign a 60% chance of the company's stock to increase by 25% in the next three months. As an astute believer in prudent risk management, you develop a pessimistic scenario assigning a 40% chance of a decline in Alpha's stock by 20% in the next three months. Based on your knowledge re cently gathered from your BBS classes you think that using options to take advantage of the market movements will be advantageous to Omega as opposed to taking a gamble with the Alpha's stock itself. You are aware that call and put options on Alpha's stock exist with six-month maturities and an exercise price of KES 90. You have also established that the quarterly compounded risk free rate is estimated at 10%.

i. What is the maximum amount you would pay for Alpha's put options today?

ii. One of the queries from the Chief Investment Officer (CIO) at Omega is "how sensitive is the call option value to changes in the price of the Alpha's stock?" Formulate a well thought response to the CIO based on the Black-Scholes-Merton (BSM) model. Assume that the stock pays dividends at a continuous dividend yield of 1.4%, the continuously compounded interest rate is 8% and the annual volatility of the Alpha's stock returns is 10%.