In this acticle the SABR model is first presented in another form ( see equation 7 in the article ) and then extended to the so called ZABR model. I have a couple of questions to help me understand the model.

  • Main question: What is the exact formula that generates the graphs in Figure 3. $IV(k)=...?$
  • in figure 1 and 2. Why on earth is $\sigma(s)=c_0s^{c_1}$?
  • What is $x$ in equation 7? I mean the financial interpretation. It will make no sense to call it the implied volatility but I am not sure.

Here is an Matlab implementation I found: https://se.mathworks.com/matlabcentral/fileexchange/50328-zabr-stochastic-volatility-smile-modelling


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