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Some equities on European markets have options traded in two different exercise styles: American and European.

Examples:

Consider constructing volatility surface for given equity with two set of options, when for each expiration/maturity there are two corresponding IV points (from European and American options respectively.)

How one in this case would construct the surface and what is the reasoning?

  • Using only one set of options (either European or American), chosen by some parameter (total volume, open interest, etc.)
  • Combining both sets
  • Something else
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If you can get anywhere close to the same open-interest and volume using European options as the corresponding American ones, you'll have a much easier time just using them.

American options with high probability of early exercise don't contain information about that back end of the vol surface, and it's kind of hard to decide just what to do with their implied vols. The only way you can be sure you've done it properly is to throw them all into some giant multivariate optimization algorithm on a parameterized volatility surface.

That said, if you're calibrating the vol surface to trade these same American options, rather than (say) to fit some exotics-pricing or risk model, then you had better calibrate to those American options.

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Frequently, American options are de-Americanized. Afterward, you "simply" use the standard model you use to construct your VOL surface based on European prices.

In reality, things are quite messy though:

  • You need data filtering to ensure the reliability of the inputs (do you use several exchanges vs most liquid, stale prices, unreliable bid-ask spreads, spikes, jumps around market open / close...)
  • Theoretically, it's easy to construct forwards from put-call parity (apart from options you could also use futures; but the maturities usually do not align, dividend futures, OTC instruments, etc). Practically, you face numerous problems though (the underlying and options may trade at different times, listed option prices can be fairly unreliable in some cases, or only one-sided markets, etc.).
  • Dividend seasonality is an issue...
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