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I believe that the right-hand side refers to options sold before CHK split its stock on Apr 15 2020 1 for 200. 1. But why do the IV differ so much, e.g. at the strike price of 3?

  1. Why hasn't this difference in IV been arbitraged?

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  • $\begingroup$ This has nothing to do with economics. There is a quantitative finance stack exchange. $\endgroup$ – Brian Romanchuk Jun 27 '20 at 12:07
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With illiquid stocks, the B/A spreads for the options are Holland tunnel wide. For some it's maybe 50 cents, for others, over $4. With such a wide range of price, where is the actual market? What's fair value on which to base an IV calculation?

Most likely, the broker is basing IV on the midpoint. However, the midpoint isn't an accurate representation of price. For example, the $8 put is 4.00/7.80 with a midpoint of 5.90. Suppose I offer to sell at 6.80? That changes the midpoint to 5.40 and therefore lowers the IV. It's all meaningless.

As for arbitraging the difference, how do you arbitrage when there's a spread of anywhere from 50 cents to over 4 dollars? It's impossible.

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