QUESTION 1 a. Using the following information, calculate the price of a 6-month long call option using a two-step binomial tree procedure. So = $10, K = $10, r = 5% (annual), o = 30% (annual). You will need the following equations: p = ad (1) a = erAt (2) u = evAt (3) d = _ (4) f = [pfu + (1 -p)fale-rat (5) (40 MARKS) b. Discuss how the binomial tree procedure can be extended so that the pricing an option with the binomial method will converge to the price given by the Black- Scholes-Merton model. (30 MARKS) c. The following image is taken from the spreadsheet 'Simple Binomial Model.xlsx'. In cell D22, the formula below is used. Explain how this formula can create a binomial tree procedure for the movement of a stock price in Excel. Binomial Call and Put Pricing with 6 steps from slides 12%% 7 T (years) 05 8 Steps 9 At (years) 0.08333 =IF(C22="", IF(C21=","",C21*$B$12),C22*$B$11) 10 Volatility 30%% 11 U 1.09046 12 d 0.91704 13 a 1.01005 14 P 0.53632 15 1- 0.46368 16 K 21 17 Discount factor 0.99005 18 19 Period 20 Time 0.000 0.083 .167 0.250 0.333 0.417 0.500 21 22 Stock 23 20 21.8093 23.7822 25.9336 28.2796 30.8379 33.6276 18.3408 20 21.8093 23.7822 25.9336 28.2796 25 16.8193 18.3408 20 21.8093 23.7822 26 15.424 16.8193 18.3408 20 27 14.1444 15.424 16.8193 28 12.971 14.1444 11.895 (30 MARKS)