Calibration and Parameter Estimation in Models › Key Parameters

Michael BrenndoerferDecember 13, 20251 min read
Quantitative FinanceAll chapters
Part 8 of 15Econometrics and Statistical Modeling
Chapter 45Calibration and Parameter Estimation in Models › Key Parameters
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The key parameters for the SABR model are:

  • α\alpha: Initial volatility level. Controls the overall height of the implied volatility ATM.
  • β\beta: Elasticity parameter. Determines the relationship between asset price and volatility (backbone). Often fixed (e.g., to 0.5) during calibration.
  • ρ\rho: Correlation between the asset price and volatility. Controls the skew (slope) of the volatility smile.
  • ν\nu: Volatility of volatility (vol-vol). Controls the curvature (convexity) of the volatility smile.