Contract Name	Last Trade Date	Strike	Last Price	Bid	Ask	Change	% Change	Volume	Open Interest	Implied Volatility
FB171117C00100000	2017-11-13 12:44PM EST	100	78.75	78.25	78.4	0	-	2	34	175.00%
FB171117C00105000	2017-11-06 10:57AM EST	105	74.49	73.3	73.7	0	-	1	1	233.59%
FB171117C00110000	2017-11-10 11:54AM EST	110	68.5	68.3	68.7	-1.53	-2.18%	5	58	215.23%
FB171117C00115000	2017-11-07 12:38PM EST	115	65.1	63.3	63.7	0	-	32	287	197.66%
FB171117C00120000	2017-11-10 3:43PM EST	120	58.4	58.35	58.7	-1.85	-3.07%	65	130	183.98%
FB171117C00125000	2017-11-13 9:31AM EST	125	52.55	53.1	53.5	0	-	1	20	164.06%
FB171117C00130000	2017-11-14 10:09AM EST	130	47.75	48.2	48.4	-1.25	-2.55%	18	378	132.03%
FB171117C00135000	2017-11-13 11:18AM EST	135	43.82	43.1	43.45	0	-	3	1,079	126.17%
FB171117C00140000	2017-11-14 12:40PM EST	140	38.65	38.1	38.45	-0.28	-0.72%	108	1,784	111.72%
FB171117C00145000	2017-11-14 9:31AM EST	145	32.87	33.2	33.45	-0.31	-0.93%	1	368	65.63

Problem 3

Choose a stock that you would like to study that has a current set of liquid put and call options. You can check whether the stock has listed options at https://finance.yahoo.com. Select a single option maturity date between 12/15/2017 and 6/15/2018, and gather data on the ten call options expiring on that date that have strike prices closest to the current stock price. The data items youll want to gather include the following: (1) strike price; (2) last trade price for each of the ten call options; (3) last trade price for the stock; (4) maturity, in years, for the ten contracts; and (5) implied volatility as reported by Yahoo Finance. (Note: if Yahoo Finance reports zero trading volume for an option contract, use the average of the contracts bid and ask prices to measure the last trade price.)

Write a formula in Excel for the Black-Scholes option value of a call, and then use either Solver or Goal Seek to calculate the implied volatility for each of the ten call options. In your calculations, you can assume the following:

Dividend yield is zero

Annualized, continuously-compounded risk-free rate is equal to the 1-year

Treasury rate (see www.treasury.gov for data).

Compare the implied volatilities you calculated against the ones reported in

Yahoo Finance. Are they the same? If not, what might explain the discrepancy?

Graph the implied volatilities for the 10 options against the moneyness of the contract (measured as the ratio of stock price to option strike price). Describe the shape of your graph. Based on the results, what can you say about market demand for the different options and about the accuracy of your Black-Scholes calculation?