Options Volatility Model SABR (z-shift). This is an implementation of the 2002 Hagan SABR model, that was originally published in Jan 2002.
There has been various adaptations over the decades, notably the addition of a z-shift to account for extreme low-rates affecting the lower zero-bound condition post-GFC.
There is currently, the closed-form implementation of the lognormal, and normal case. There is also a sabr calibration-fit function, though enabled *** without *** beta fit.
Experienced SABR practitioners should be able to derive the beta parameter from historical analysis, as necessary for their respective markets.
Hagan, Patrick S.; Kumar, Deep; Kesniewski, Andrew S.; Woodward, Diana E. (January 2002). "Managing Smile Risk" (PDF). Wilmott. Vol. 1. pp. 84–108. Archived (PDF) from the original on 2022-04-30. Retrieved 2022-04-30.
The request.get function for *** 'sabr_hist' *** allows user to access the 5-latest rolling saved-down SABR parameters for both the BTC, and ETH vanilla options. Note that the calibration is based off beta = 0.90, and under lognormal model.
The request.get function for *** 'local_hist' allows user to access the 5-latest rolling saved-down Local Volatility parameters. The 3-degree polynomial fit takes in
a) strikes > 0.5 * forward, and strikes < 2.0 * forward
b) fitted across both expiry, and strike space.
As such, due to the discontinuty surface for the very short-dated expiries, error-fitting is quite large for < 1week, and progressively gets better for longer-expiries. Note that local-Volatility model fit does not explicitly fit to ATMF implied vols, similar to that of the SABR fit.
