The S&P 500 index closes at 2000. European call and put options on the S&P 500 index with the exercise prices show below trade for the following prices:

EXERCISE PRICE	$1,950	$1,975	$2,000	$2,025	$2,050
CALL PRICE	$88	$66	$47	$33	$21
PUT PRICE	$25	$26	$32	$44	$58

All options mature in 88 days. The S&P 500 portfolio pays a continuous dividend yield of 1.56% per year and the annual yield on a Treasury-Bill which matures on the same day as the options is 4.63% per year. Determine what is the implied volatility of each of these calls and puts (self study: implied volatility is the standard deviation computed not from historical data (i.e. the standard deviation of the natural logarithms of the ratios of consecutive stock prices for continuous returns), but directly from the B-S formula by plugging in all other variables. The easiest way to solve implied volatility for options in Excel is by using the Excel Solver. You should plug in the options data as input and ask to solve the standard deviation as the output that solves for the specific option prices. You may also try to use the Excel macro ivol for implied volatility, but see if you can find it online). What pattern do these implied volatilities follow across exercise prices and between calls vs. puts?