Why American Option Implied Volatilities Can Diverge Across Moneyness

Summary

The document raises a question about differing implied volatilities inferred from in-the-money and out-of-the-money American equity options. The observed pattern comes from reversing an American option pricing model against market prices, with put-call parity used to estimate an at-the-money reference. It asks why in-the-money contracts may appear relatively expensive and how the lack of European-style put-call parity affects the comparison.

The text supplies no answer or supporting derivation, so it does not establish that the reported pattern is general or explain its cause. Its useful takeaway is that American exercise rights complicate direct call-put implied-volatility comparisons: early exercise and dividends can affect prices, and an implied volatility depends on the pricing model and inputs. The observation is tied to one stock analysis and should not be treated as evidence of a universal volatility skew.

Key ideas

• American options do not satisfy the same put-call parity relation as European options.
• The document reports a perceived implied-volatility difference between in-the-money and out-of-the-money American options.
• Early exercise rights and dividends can influence American option prices and model-implied volatility.
• The reported pattern is an observation without a derivation or evidence that it generalizes.

Tags

# Implied Volatility Discrepancy in American Options - Mathematical Reasoning?


# Implied Volatility Discrepancy in American Options - Mathematical Reasoning?












I've been analyzing Tesla stock American options data and have observed an interesting pattern that I'd appreciate some help understanding.

For this analysis, I obtained the Implied Volatilities (IVs) by reversing the Binomial Option Pricing model specific to American options and used the current market price derived via PCP at atm.

Unlike European options, where we know that the In-The-Money (ITM) Implied Volatility (IV) of the put side equals the Out-Of-The-Money (OTM) IV of the call side and vice versa, American options seem to behave differently.

In the case of American equity options, it appears to be such that:

IV of ITM Call side > OTM Put side IV of ITM Put side > OTM Call side For clarity, I've attached an image plot that illustrates this:

While I'm aware of the fact that Put-Call Parity does not hold in American options, causing implied IVs for calls and puts to diverge, I'm struggling to understand the mathematical reasoning that leads to ITM options generally being pricier.

Could someone explain why this might be the case? Any insights into the mathematics or logic behind this observed pattern would be greatly appreciated.

Thank you.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.