Volatility smile or volatility skew refers to the relation between implied volatility and strike price. Quotes for selected options on Facebook stock on April 17, 2020 are provided below. Determine implied volatility for call options and plot as a function of the strike price. Use midpoint of the bid and ask quotes for the stock price and for option price. Facebook does not pay dividends. Assume the interest rate is 0.5% per annum with annual compounding (not continuous compounding). The expiration date of all options is June 19, 2020. To determine implied volatility, input all parameters in Black-Scholes formula and adjust volatility until the price given by formula matches the price quote. If you use Excel, Goal Seek function can be helpful. The Excel formula =DAYS(DATE(2020,6,19),DATE(2020,4,17)) returns the number of days to expiration.

Facebook, Inc. Class A Common Stock DATA AS OF APR 17, 2020 $179.24 2.99 1.7% FB > FB OPTION CHAIN Facebook, Inc. Class A Common Stock (FB) Option Chain MONTH JUN 2020 DATE 06/19/2020 CALLS LAST CHANGE BID ASK V OLUME OPEN INT STRIKE LAST CHANGE I D ASK VOLUME OPENINT 165.00 7.10 1.22 6.20 7.05 86 4763 21.00 18.04 2.88 1,83 20.35 17.25 22.05 18.25 49 71 2700 5183 170.00 8.37 1.43 8.10 3.65 188 12909 14.55 1.20 14.20 14.80 212 4915 175.00 10.45 1.40 10.00 10.55 1 54 9635 11.65 1.16 11.45 12.00 799 9107 180.00 12.75 -3.25 12.10 12.70 279 7582 9.20 -0.90 8.60 9.60 380 5527 105.00 15.30 1.37 14.25 15.30 79 6090 6.91 -0.56 6.80 7.20 4 04 8996 190.00 17.72 21.95 3.08 .3.51 17.35 20.15 10.20 22.35 56 23 8284 6134 5.22 +0.57 4.65 5.85 584 5365 195.00 EXPIRES: 06/19/2020 LAST TRADE: $179.24 (AS OF APR 17, 2020) Facebook, Inc. Class A Common Stock DATA AS OF APR 17, 2020 $179.24 2.99 1.7% FB > FB OPTION CHAIN Facebook, Inc. Class A Common Stock (FB) Option Chain MONTH JUN 2020 DATE 06/19/2020 CALLS LAST CHANGE BID ASK V OLUME OPEN INT STRIKE LAST CHANGE I D ASK VOLUME OPENINT 165.00 7.10 1.22 6.20 7.05 86 4763 21.00 18.04 2.88 1,83 20.35 17.25 22.05 18.25 49 71 2700 5183 170.00 8.37 1.43 8.10 3.65 188 12909 14.55 1.20 14.20 14.80 212 4915 175.00 10.45 1.40 10.00 10.55 1 54 9635 11.65 1.16 11.45 12.00 799 9107 180.00 12.75 -3.25 12.10 12.70 279 7582 9.20 -0.90 8.60 9.60 380 5527 105.00 15.30 1.37 14.25 15.30 79 6090 6.91 -0.56 6.80 7.20 4 04 8996 190.00 17.72 21.95 3.08 .3.51 17.35 20.15 10.20 22.35 56 23 8284 6134 5.22 +0.57 4.65 5.85 584 5365 195.00 EXPIRES: 06/19/2020 LAST TRADE: $179.24 (AS OF APR 17, 2020)