1. 1. 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 Black-Scholes using the average of the 5^th and 6^th columns prices, i.e. bid and ask prices, in the attached figure. (4)

 

 

 

 

SPX, Expiration: 2023, Dec 29
K (Strike Price)	4600 (past 1 year  ?)	4600(past 6 month  ?)
50 steps Price
Call
Put
100 steps Price
Call
Put
Black Scholes  Price
Call	82.98	57.05
Put	39.09	13.17
implied volatility
Call		X
Put		X

 

 

 

Image transcription text

SPXW231229C04580000 2023-11-24 12:42PM 4,580.00 55.20 49.00 49.80 0.00 EST SPXW231229C04585000 2023-11-24 12:49PM 4,585.00 52.69 46.50 47.30 0.00 EST SPXW231229C04590000 2023-11-24 11:35AM 4,590.00 51.00 44.20 45.00 0.00 1 EST SPXW231229C04595000 2023-11-24 10:57AM 4,595.00 49.39 41.70 42.50 0.00 EST 10 SPXW231229C04600000 2023-11-26 8:23PM EST 4,600.00 42.40 39.50 40.30 3.20 -7.02% SPXW231229C04605000 2023-11-24 12:56PM 4,605.00 EST 43.70 37.30 38.10 0.00 SPXW231229C04610000 2023-11-24 12:10PM 4,610.00 40.80 35.30 EST 36.00 0.00 

Image transcription text

EST SPXW231229P04595000 2023-11-24 12:10PM 4,595.00 67.30 72.60 73.40 0.00 EST
SPXW231229P04600000 2023-11-24 12:53PM 4,600.00 69.80 75.30 76.20 0.00 EST
SPXW231229P04605000 2023-11-24 12:10PM EST 4,605.00 72.50 78.10 78.90 0.00