SABR and Heston Model

[dacronje]

Hello All,

I am try to construct the volatility surfaces for both the SABR and Heston Models in Matlab. I was just wondering what market information one requires to construct volatility surfaces for both of these models.

i.e. future prices and at the money volatilities for the SABR model (do I need anything else)

Thank you for any help

 

[dacronje]

I have read quite a few articles on constructing the volatility surface such as this one. And many other. Not 100% on how the calculate the beta parameter using the log-log plot. Do I do a regression on the data in the plot to calculate the gradient and from there calculate the beta value (gradient=-(1-beta)) ?

Once again any help will be appreciated.
Thank you

 

[financeguy]

Although a lot of the literature suggests running regressions to find beta, these regressions are often unstable and can lead to betas outside of [0,1]. Practitioners normally fix beta to 1/2 or 1 and calibrate the other parameters. The other option is to make it a calibrated parameter and use more points on the smile to minimize squared error against.