theoretical numbers ^ vol surface

After you work in volatility field for a while, you may figure out when (and when not) to use the word “theoretical”. There’s probably no standard definition of it. I guess it basically means “according-to-BS”. It can also mean risk-neutral. All the greeks and many of the pricing formulas are theoretical.

The opposite of theoretical is typically “observed on the market”, or adjusted for skew or tail.

Now, the volatility smile, the volatility term structure and the vol surface are a departure from BS. These are empirical models, fitted against observed market quotes. Ignoring outliers among raw data, the fitted vol surface must agree with observed market prices — empirical.

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