Consider a stock currently priced at $50. You are seeking to calculate the volatility skew/smirk for...

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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. 1 PARAMETERS 2 sigma 3 delta t 345678 888ರ ಹರ ದ ಹ ದ ನ - 5 0 0 - € 5 d 6 r 7 8 9 16 18 19 20 u 22 21 Sum 23 p Stock price (S) Strike (K) 176543NLO 2 0 B 0.22 0.0040 1.0140 0.9862 0.08 0.5080 50 48 # paths 1 7 21 35 35 21 7 1 C D E RN probs Stock price @ T 55.094 53.588 52.123 50.698 49.312 0.0087 0.009 0.0085 0.059 0.0082 0.172 0.0079 0.278 0.0077 0.269 0.0074 0.156 0.0072 0.050 0.0070 0.007 1 47.964 46.653 45.377 F G PV Payoff H Call Exp value 7.094 0.062 5.588 0.331 4.123 0.709 2.698 0.749 1.312 0.353 0.000 0.000 0.000 0.000 0.000 0.000 2.2032 2.1983 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. 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. 1 PARAMETERS 2 sigma 3 delta t 345678 888ರ ಹರ ದ ಹ ದ ನ - 5 0 0 - € 5 d 6 r 7 8 9 16 18 19 20 u 22 21 Sum 23 p Stock price (S) Strike (K) 176543NLO 2 0 B 0.22 0.0040 1.0140 0.9862 0.08 0.5080 50 48 # paths 1 7 21 35 35 21 7 1 C D E RN probs Stock price @ T 55.094 53.588 52.123 50.698 49.312 0.0087 0.009 0.0085 0.059 0.0082 0.172 0.0079 0.278 0.0077 0.269 0.0074 0.156 0.0072 0.050 0.0070 0.007 1 47.964 46.653 45.377 F G PV Payoff H Call Exp value 7.094 0.062 5.588 0.331 4.123 0.709 2.698 0.749 1.312 0.353 0.000 0.000 0.000 0.000 0.000 0.000 2.2032 2.1983 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.

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a The highlighted section of the spreadsheet calculates the value of the European call option using riskneutral pricing principles Lets go through each column Column A This column represents the numbe... View the full answer