SABR Calibration in Python

10 Pages Posted: 1 Feb 2016

Date Written: January 31, 2016


This work is to implement in Python the SABR volatility model for swaptions and its calibration. The attached script takes market data of forward rates and swaption volatilities, then calibrates the parameters in order to get the implied volatilities.

Formulas are given by Hagan et al. (2002), it is provided also the "shifted model" to overtake negative forward rates' problem.

You can download the script (, and the market data example online (MarketData.xlsx).

This paper consists in the explanation of the commands to have reason of computations and final results.

Keywords: SABR, Python, calibration, shift, implied volatility, swaptions

Suggested Citation

Travaglini, Giovanni, SABR Calibration in Python (January 31, 2016). Available at SSRN: or

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