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

All options mature in 88 days. The S&P 500 portfolio pays a continuous dividend yield of 1.47% per year and the annual yield on a Treasury Bill which matures on the same day as the options is 5.02% per year. Determine what is the implied volatility of each of these calls and puts. What pattern do these implied volatilities follow across exercise prices and between calls vs.
puts?

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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