please answer all parts of the question.

5. (15 points) Today, the SPX, a security based on the S&P 500 index, is traded at $1275. The European call and put options on SPX with the exercise prices are traded at the following prices Exercise Price Call Price Put Price $1,240 $40.0 $14.0 $1,280 $17.0 $30.0 All options mature in 58 days and the current interest rate of the 3 month Treasury Bill is 1.57%. If one year is assumed to be 365 days, answer the following questions: a. Calculate the standard deviation (called implied volatility) of each of these call and put options. b. What is the average of the implied volatility of the 4 options? E F G H a Call Put A B D 1 Problem 5 2 Black Sholes Option Pricing - Implied Volatility 3 4 S&P 500 5 Stock Price 6 Risk Free rate 7 Time to Maturity 8 Standard Deviation 9 10 Exercise Price $1,240 $1,280 11 Call Price 12 Put Price 13 14 15 0.000 0.000 0.0000 b Call $1,240 $1,280 Put $1,240 $1,280 16 Option Type 17 Exercise Price 18 Standard Deviation 19 20 Observed Option Price 21 BS Option Prices 22 23 24 A. Implied Volatility 25 Exercise Price 1240 1280 26 Call 27 Put 28 29 30 B. 31 Volatility average 32 33 5. (15 points) Today, the SPX, a security based on the S&P 500 index, is traded at $1275. The European call and put options on SPX with the exercise prices are traded at the following prices Exercise Price Call Price Put Price $1,240 $40.0 $14.0 $1,280 $17.0 $30.0 All options mature in 58 days and the current interest rate of the 3 month Treasury Bill is 1.57%. If one year is assumed to be 365 days, answer the following questions: a. Calculate the standard deviation (called implied volatility) of each of these call and put options. b. What is the average of the implied volatility of the 4 options? E F G H a Call Put A B D 1 Problem 5 2 Black Sholes Option Pricing - Implied Volatility 3 4 S&P 500 5 Stock Price 6 Risk Free rate 7 Time to Maturity 8 Standard Deviation 9 10 Exercise Price $1,240 $1,280 11 Call Price 12 Put Price 13 14 15 0.000 0.000 0.0000 b Call $1,240 $1,280 Put $1,240 $1,280 16 Option Type 17 Exercise Price 18 Standard Deviation 19 20 Observed Option Price 21 BS Option Prices 22 23 24 A. Implied Volatility 25 Exercise Price 1240 1280 26 Call 27 Put 28 29 30 B. 31 Volatility average 32 33