Calibrating Heston to Market Options Without a Prior Surface

Summary

The document asks whether Heston model calibration requires first constructing a smoothed, arbitrage-free implied volatility surface, as is commonly needed in local volatility work. The accepted response describes Heston calibration as fitting model parameters directly to observed market option quotes through a minimization exercise. In this framing, the calibrated parameters generate the model’s implied surface, so a separately regulated surface is not presented as a prerequisite.

The key distinction is between the models’ purposes: the response says local volatility relies on an arbitrage-free implied volatility surface to ensure uniqueness, whereas Heston calibration is treated as fitting a parametric model to sparse market data. The discussion is brief and offers no calibration objective, parameter constraints, dataset, numerical example, or empirical comparison. It therefore provides a conceptual distinction rather than a complete implementation recipe; practical calibration quality and the handling of noisy or inconsistent quotes remain unaddressed.

Key ideas

• Heston parameters can be calibrated by minimizing differences between model values and market option quotes.
• The fitted Heston parameters determine the model’s implied volatility surface.
• The response distinguishes this workflow from local volatility, which it says needs an arbitrage-free surface for uniqueness.
• The document does not specify an objective function, quote filtering method, or empirical calibration results.

Tags

# Does the Heston calibration have to be done on an arbitrage-free surface?


# Does the Heston calibration have to be done on an arbitrage-free surface?












In a similar way to local volatility? I'm trying to calibrate a surface, but the results aren't convincing, so I was wondering if it was necessary to first use a way to regulate it (splines, regressions), then calibrate the Heston model, or if it was necessary to calibrate first the model on the few data, then get a surface.

## Answer by Benedict (score 1, accepted)

https://quant.stackexchange.com/a/50239

Apparently your heston model parameters should define the surface. You're fitting to options quoted in the market, thus a minimization exercise. Not like local vol, where it needs a abitrage free implied vol surface to garantee uniqueness

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