# Understanding the ZABR model (an extension of SABR)

http://janroman.dhis.org/finance/SABR/ZABR%20Andreasen.pdf

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