2. Please download SPX closing prices for the past 1 year. Suppose today is the 2023 Nov 24 market close. S\&P 500 INDEX (^SPX) Historical Data - Yahoo Finance a. Based on downloaded closing stock price, compute the annulized volatility of SPX () based on (1) past 1 year, (2) past 6 months. b. Use Libor USD one month interest rate (4.8\%, monthly compounding), compute the SPX options prices listed in the table. (Note: convert rate to continuous compounded rate). The maturity of the options is [(calendar days to expiration)/ 365], or trade days to expiration/252 c. Compute the implied volatility of options listed in the table based on BlackScholes using the average of the 5th and 6th columns prices, i.e. bid and ask prices, in the attached figure. (4) SPX, Expiration: 2023, Dec 29 \begin{tabular}{|l|c|c|} \hline K (Strike Price) & \begin{tabular}{c} 4600 (past 1 \\ year ) \end{tabular} & \begin{tabular}{c} 4600 (past 6 \\ month ) \end{tabular} \\ \hline 50 steps Price & & \\ \hline Call & & \\ \hline Put & & \\ \hline & & \\ \hline 100 steps Price & & \\ \hline Call & & \\ \hline Put & & \\ \hline & & \\ \hline Black Scholes Price & 82.98 & 57.05 \\ \hline Call & 39.09 & 13.17 \\ \hline Put & & \\ \hline & & \\ \hline implied volatility & & X \\ \hline Call & & \\ \hline Put & & \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} \hline & & & & & & & & & & \\ \hline & SPXW231229 & C04580000 & \begin{tabular}{r} 2023112412:42PM \\ EST \end{tabular} & 4,580.00 & 55.20 & 49.00 & 49.80 & 0.00 & - & \\ \hline & SPXW231229 & C04585000 & \begin{tabular}{r} 20231124 12:49PM \\ EST \end{tabular} & 4,585.00 & 52.69 & 46.50 & 47.30 & 0.00 & - & \\ \hline & SPXW231229 & C04590000 & \begin{tabular}{r} 20231124 11:35AM \\ EST \end{tabular} & 4,590.00 & 51.00 & 44.20 & 45.00 & 0.00 & & 1 \\ \hline & SPXW231229 & C04595000 & \begin{tabular}{r} 20231124 10:57AM \\ EST \end{tabular} & 4,595.00 & 49.39 & 41.70 & 42.50 & 0.00 & & 10 \\ \hline & SPXW231229 & C04600000 & \begin{tabular}{r} 202311268:23PM \\ EST \end{tabular} & 4,600.00 & 42.40 & 39.50 & 40.30 & -3.20 & 7.02% & \\ \hline & SPXW231229 & C04605000 & \begin{tabular}{r} 2023112412:56PM \\ EST \end{tabular} & 4,605.00 & 43.70 & 37.30 & 38.10 & 0.00 & & 2 \\ \hline & SPXW231229 & C04610000 & \begin{tabular}{r} 20231124 12:10PM \\ EST \end{tabular} & 4,610.00 & 40.80 & 35.30 & 36.00 & 0.00 & & 4 \\ \hline & & & ESI & & & & & & & \\ \hline SPXW231229P0 & 04595000 & 2023-11-2 & \begin{tabular}{r} 24 12:10PM \\ EST 4,595. \end{tabular} & .00 & 67.30 & 72.60 & 73.40 & & 00 & \\ \hline SPXW231229P0 & 04600000 & 2023-11-2 & \begin{tabular}{r} 24 12:53PM \\ EST \end{tabular} & .00 & 69.80 & 5.30 & 76.20 & 0.0 & 00 & \\ \hline SPXW231229P0 & 04605000 & 2023112 & \begin{tabular}{r} 24 12:10PM \\ EST \end{tabular} & .00 & 72.50 & 78.10 & 78.90 & & 00 & \\ \hline \end{tabular}