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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: Exercise price 1,950 1,975 2,000 12,025 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. What pattern do these implied volatilities follow across exercise prices and between calls vs. puts? 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: Exercise price 1,950 1,975 2,000 12,025 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. What pattern do these implied volatilities follow across exercise prices and between calls vs. puts