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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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  • $\begingroup$ Cubic splines should be easy to fit. Have a look at gstheral's svi paper, there are several parameterisations in there thst might be of interest to you. $\endgroup$
    – will
    Commented Feb 23, 2020 at 18:33

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