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By what rule does the CBOE determine the available strikes for puts and calls on the SPX? The contract specification (http://www.cboe.com/products/stock-index-options-spx-rut-msci-ftse/s-p-500-index-options/s-p-500-options-with-a-m-settlement-spx/spx-options-specs) says

Strike Prices: In-,at- and out-of-the-money strike prices are initially listed. New series are generally added when the underlying trades through the highest or lowest strike price available.

Note that I am specifically not looking for traded options, but theoretically available options. I do have a dataset of option prices available, but options that have never been traded are not included.

Instead, I am looking for the initial minimum and maximum strike that CBOE makes available, and the added strikes that are created when the underlying trades through the initial bracket.

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If you download the daily EOD Quote File for SPX from the CBOE web site https://datashop.cboe.com/option-quotes you will be able to see for every expiration the highest and lowest available strike, including strikes that have no trading or no open interest. However, it could be a big job to process all the data for every trading day for a long period of time.

By the way, in my experience the exchange introduces new options before the underlying crosses the highest or lowest available strike. In years of trading I never remember a situation where there was only one strike above or below the current SPX and you had to wait for more to be introduced.

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