QUESTION 4 (3+3+3+1 = 10 MARKS) Consider a stock currently priced at $50. You are seeking to calculate the volatility skew/smirk for European options on the stock that have 7 days to maturity using the binomial option pricing model. To assist you with this, consider the following spreadsheet that seeks to price a European call with a strike of $48. The spreadsheet assumes a volatility of 22% p.a. and a constant risk-free rate of 8% p.a. continuously compounded. A B C D E F G H PARAMETERS 2 sigma 0.22 3 delta t 0.0040 4 u 1.0140 5 d 0.9862 6 r 0.08 7 p 0.5080 8 Stock price (S) 50 Strike (K) 48 10 11 Call 12 # paths RN probs Stock price @ T Payoff Exp value 13 0.0087 0.009 55.094 7.094 0.062 14 0.0085 0.059 53.588 5.588 0.331 15 21 0.0082 0.172 52.123 4.123 0.709 16 OHNWAUAV- 35 0.0079 0.278 50.698 2.698 0.749 17 35 0.0077 0.269 49.312 1.312 0.353 18 21 0.0074 0.156 47.964 0.000 0.000 0.0072 0.050 46.653 0.000 0.000 0.0070 0.007 45.377 0.000 0.000 21 Sum 1 2.2032 22 PV 2.1983 23 a) Using risk neutral pricing principles, carefully explain how the spreadsheet calculates the value of the European call option. Your discussion should focus on explaining all the columns in the highlighted section of the spreadsheet. b) Explain how you could slightly modify the spreadsheet and use solver to extract the implied volatility of the European option with a strike of $48. c) Using your modified spreadsheet as outlined in part b), explain how you would then go about constructing the volatility skew/smirk for a 7-day maturity. d) Outline one reason why you may expect to see a skew/smirk