1. Please download SPX closing prices for the past 1 year. Suppose today is the 2023 Nov...
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Question:
- 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 5th and 6th 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
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Authors: Eugene Brigham, Michael Ehrhardt, Jerome Gessaroli, Richard Nason
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