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	$1950	$1975	$2000	$2025	$2050
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 (self study: implied volatility is the standard deviation computed not from historical data, but directly from the B-S formula by plugging in all other variables. You may also try to use the Excel macro “ivol” for implied volatility)of each of these calls and puts. What pattern do these implied volatilities follow across exercise prices and between calls vs. puts?