Calibrating the Heston Model to Option Prices or Implied Volatility

Summary

The document asks why Heston models are often calibrated to implied volatilities rather than directly to option prices. Its answer is that the two targets can be converted into one another using the Black–Scholes pricing relationship: an implied volatility yields a corresponding market price, and a market price yields an implied volatility. Calibration software such as QuantLib may handle this conversion internally.

The choice of target also depends on the calibrator and the loss function. A typical procedure selects Heston parameters to minimize differences between model outputs and market observations, for example with an absolute-error or squared-error measure. The brief exchange offers no empirical comparison of calibration outcomes and does not discuss how weighting, quote quality, or market conventions affect the choice. It therefore explains equivalence in principle, rather than establishing that the two approaches behave identically in every practical calibration.

Key ideas

• Implied volatility and option price are convertible representations of the same option quote under a pricing model.
• Calibration libraries may perform the conversion between prices and implied volatilities automatically.
• A calibrator can fit Heston parameters by minimizing a chosen error measure against market observations.
• The choice of calibration target and error metric can depend on the implementation.

Tags

# Heston model calibration to option prices and implied volatility


# Heston model calibration to option prices and implied volatility












I hope that you are having a great day,

I am trying to write a research paper on the Heston model deep calibration. I noticed during my literature review that the most common approach is to calibrate the model to implied volatility and not option prices. What is the rationale behind this ?

Thanks a lot

## Answer by user78712 (score 1)

https://quant.stackexchange.com/a/81268

Implied volatility and option prices can be used interchangeably. Given the implied vol, you can find the market price using Black-Scholes formula (and vice versa).

If you are using Quantlib functions for calibration, it will do the translation for you.

Edit: Also depending upon the calibrator either can be used. Typically the calibration process attempts to find parameters for the Heston model that minimise the difference (for example the mean absolute difference or mean squared difference) between the prices produced by calibrated model parameters and the market prices.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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