a. What is the price of a European call option on a dividend paying stock when the stock price is $54, and the exercise price is $64. The option expires in 45 days, risk free rate is 5% for 45 days and 3.5% for 25 days, volatility is 25% and dividend of $2.5 to be paid in 25 days time. Assume that there are 365 days in 1 year. (20 marks)

b. Assume that a share is traded for S$855. There will be a dividend payout of S$16 after 2.5 months. The risk free interest rate is currently 5% p.a. for the next 2.5 months and 7% p.a. for the next 10 months from today (both are continuous compounded rates). If the 10-month market forward price for the stock is currently S$900. Is there an arbitrage opportunity and if so, how will you exploit the arbitrage? (State your actions and calculate the arbitrage profits) (30 marks)