Local Volatility Calibration and Risk-Neutral Drift

Summary

The document clarifies how implied volatility surfaces relate to calibrating a local volatility model to vanilla options. It explains that calibrating to vanilla option prices and calibrating to their implied volatilities are equivalent descriptions of the same market information; a complete implied volatility surface is the input used to derive the local volatility function.

It distinguishes real-world drift from the drift used in option pricing. The real-world drift belongs to the underlying asset, while pricing under the risk-neutral measure uses a risk-neutral drift that does not vary by derivative type. The response points to put-call parity as a way to infer that pricing drift. It gives no worked derivation or discussion of practical complications such as dividends, rates, or market frictions, so the explanation is conceptual rather than a full calibration recipe.

Key ideas

• A complete implied volatility surface provides the vanilla option information used to derive local volatility.
• Calibrating to vanilla prices is equivalent to calibrating to their implied volatilities.
• The real-world drift describes the underlying asset and is not specific to a derivative product.
• Option pricing uses the risk-neutral drift, which can be inferred from put-call parity.

Tags

# Drift of Local Volatility Model - Dupire


# Drift of Local Volatility Model - Dupire












i understand that the local volatility function can be computed from the implied volatility surface.(i.e there is no calibration to option prices, we just need the full implied volatility surface only)

In the standard Local vol BS Model, there is also a drift and dividend term, how do we know what values they should be?

Would they be product specific?

Best Regards, Ben

## Answer by user34971 (score 1)

https://quant.stackexchange.com/a/40991

To be honest I am not sure you understand:

- Calibrating to vanilla option prices is equivalemt to calibrating to implied volatilities. Vanilla option prices = implied vol surface

- The real world drift does not matter and is certainly not derivative product specific, it's the drift of the underlying asset. For options pricing the risk-neutral drift matters, and that is also not dependent on the type of derivative.You can infer the risk neutral drift from put call parity.

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