Question 5 (total out of 16 marks) Using the two-step binomial option pricing model calculate the price for a 2 year European call option for a stock trading at $128 today, under the following market conditions: The continuously compounded risk free rate is 0.87%pa The number of periods is 2, each of 1 year The strike price is $130 The standard deviation of the stock is 37%pa The first dividend of $1.90 is received at the end of the first year The second dividend of $2.10 is received at the end of the second year (Hint: To answer this question it is suggested you copy and complete the binomial tree into your answer booklet) M a. To four decimal places, what is the proportional increase in price of the stock at each step in the binomial tree? (1 mark) b. To four decimal places, what is the proportional decrease in price of the stock at each step in the binomial tree? (1 mark) c. To 4 decimal places, what is the probability that the stock increases in price? (1 mark) d. To 2 decimal places, calculate the price of the stock at each node on the binomial tree both before and after the dividends are paid (5 marks) e. To 2 decimal places, calculate the value of the call option at expiry (2 marks) f. To 2 decimal places, calculate the value of the call option 1 year from now (4 marks) g. To 2 decimal places, calculate the value of the call option today (2 marks)