Why SVI Calibration Can Fit Option Prices or Implied Volatility

Summary

The document asks whether an SVI volatility surface should be calibrated to option prices or to implied volatility or total variance. The answer emphasizes that option prices are the market observations from which implied volatilities are derived, and that different methods may produce implied volatilities from the same prices. The calibration ultimately matters insofar as it reproduces the traded prices.

The response offers a practical equivalence: if fitting implied volatility reproduces the same option prices accurately, then the choice of fitting prices or implied volatility may not matter. This is a brief, qualitative answer rather than a numerical comparison of objective functions or calibration outcomes. It does not discuss weighting, bid-ask spreads, sensitivity across strikes and expiries, or how price errors translate into volatility errors. Those omissions limit its usefulness as a full calibration recipe; it mainly clarifies the principle that market prices are the underlying target and that an implied-volatility fit can be adequate when it preserves those prices.

Key ideas

• Option prices are the market data from which implied volatilities are calculated.
• Different implied-volatility calculation methods can represent the same observed option prices.
• Fitting implied volatility can be acceptable if it reproduces option prices accurately.
• The response gives no numerical comparison or guidance on calibration weighting.

Tags

# SVI calibration, why fit to option prices and not implied volatilities


# SVI calibration, why fit to option prices and not implied volatilities












Bear with me. Related (very good) question: How to calibrate a volatility surface using SVI

From this paper http://arxiv.org/pdf/1204.0646.pdf, page 21.

Why does the recipe suggest fitting to option prices rather than simply working with implied total variance?

Is there actually any (numerical?) point in working with option prices rather than impl vols or total implied variance?

## Answer by hotsource (score 2, accepted)

https://quant.stackexchange.com/a/21619

Different methods exists to compute implied vol from the same option prices, eventually it's prices that matters to calibration. But if you can reproduce same option prices accurate to the cent by fitting implied vol, I think it doesn't matter.

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