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Calibrating SABR to Quoted Option Prices or Implied Volatility

Article Quant Q&A · Author: Sinja
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Summary

The document explains calibration in the context of using the SABR stochastic volatility model to price foreign exchange call options. Calibration means choosing model parameters so that model outputs match observed market quotes as closely as possible. The response describes two possible fitting targets: quoted option prices and implied volatilities derived from those prices.

The question asks whether parameters can instead be estimated from historical price data, but the answer does not address that comparison directly. It provides no objective function, weighting scheme, calibration procedure, market data example, or evidence comparing the two fitting targets. It therefore offers a basic definition rather than a full implementation guide. The material is limited to the general idea of matching model prices or implied volatilities to quoted values, and it does not specify which approach is preferable for a particular market or use case.

Key ideas

  • Calibration selects model parameters to bring model outputs close to observed option quotes.
  • The fitting target can be option prices or implied volatilities.
  • The document frames calibration around SABR pricing of foreign exchange options.
  • It does not explain historical-data estimation or provide a concrete fitting algorithm.

Tags

ForexOptionsVolatilityDerivatives pricing
Full text
# How does one calibrate a stochastic volatility model?


# How does one calibrate a stochastic volatility model?












I will try to use SABR Model to price call options in FX market. What does it mean to calibrate the model? As far as my understanding of the Wikipedia article goes, it means to estimate the parameters. In this case: Alpha, Beta and the correlation of the wiener process. Have I understood correctly?

If yes, Can I estimate the parameters from price history or does it have to option prices?

Thanks! Sanjay, India

## Answer by user16651 (score 3)

https://quant.stackexchange.com/a/28070

Indeed parameters are selected so that the quoted option prices are as close as possible to the model option prices. Alternatively, quoted and model implied volatilities can be used instead of prices.The first category are those that minimize the error between quoted and model. The second category,are those that minimize the error between quoted and model implied volatilities.

You can use these

- http://www.mathworks.com

- SABR Implied Volatility and Option 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.