Skip to content
All library documents

Mapping a Calibrated SABR Model to an Implied Volatility Smile

Article Quant Q&A · Author: Sanjay
Read the original

Summary

The question asks how calibrated SABR parameters can be turned into points on a strike-versus-volatility graph. The concise answer gives a practical sequence: use the calibrated model parameters to calculate option prices at a selection of strikes, then invert those prices through the Black–Scholes framework to obtain implied volatilities. Plotting each strike against its corresponding implied volatility produces the smile or skew.

The reply treats this as a straightforward calculation once calibration is available, and does not provide equations, code, or a numerical example. It also does not discuss choices such as option maturity, market conventions, strike range, or the suitability of Black–Scholes implied volatility as the reporting measure. The method therefore explains the basic mapping workflow, while leaving implementation details and validation to the practitioner.

Key ideas

  • A calibrated SABR model can price options at selected strikes.
  • Convert each model price to a Black–Scholes implied volatility to create a strike-volatility point.
  • Plotting those points shows the model's implied volatility smile or skew.
  • The answer omits implementation details and does not assess conventions or calibration quality.

Tags

OptionsVolatilityDerivatives pricingForex
Full text
# SABR model: from calibration to mapping the smile/skew in a graph


# SABR model: from calibration to mapping the smile/skew in a graph












Let's say that I have a calibrated SABR model in FX market (eg for Eurodollar options). So I have estimated values of beta, rho, alpha, and vol of vol. How do I map the calibration in a (strike, vol)-graph. How mathematically challenging would that process be?

## Answer by dm63 (score 2, accepted)

https://quant.stackexchange.com/a/28270

You would simply calculate the prices of various strike options using your parameters, then calculate the black scholes implied vol of each option. Did I miss the point of your question ?

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.