Five-Parameter Volatility Surface Fitting for Options Market Making

Summary

The document poses a model-selection problem for options market making: represent a volatility surface with five inputs, described as maximum put and call levels, skew, curvature, and at-the-money volatility. The author says the SABR model does not flex enough to fit every observed volatility curve, while cubic splines have been difficult to calibrate. The central question is whether a mathematical function can reproduce an arbitrary surface using only those five degrees of freedom.

No answer, calibration procedure, empirical comparison, or evidence of a model’s fit is provided. The question highlights a tension between compact parameterization and flexibility: five inputs may be convenient operationally, but an arbitrary market surface may require more freedom. The document therefore frames a modeling challenge rather than establishing a recommended approach. Any proposed method would need to specify what the five controls mean, how the surface is calibrated, and how fit quality and stability are assessed.

Key ideas

• The author seeks a volatility surface representation controlled by five market-facing parameters.
• The proposed controls are put and call extremes, skew, curvature, and at-the-money volatility.
• The author reports limited flexibility with SABR and difficulty calibrating cubic splines.
• The document supplies no solution or validation, so it does not establish that five parameters can fit arbitrary surfaces.

Tags

# Vol surface fitting with 5 degrees of freedom


# Vol surface fitting with 5 degrees of freedom












For an options market making operation I need to be able to build a volatility surface, based on only 5 degrees of freedom, like e.g.: MaxPut, MaxCall, Skew, Curve and At The Money Vol.

Is there an existing model or mathematical function, that is able to replicate any given vol surface by using just these 5 degrees of freedom?

I am currently using the SABR model, but it cannot adjust to any vol curve. I have used Cubic Splines, but it is really difficult to calibrate it.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.