What is the relationship between SABR parameters $\sigma, \alpha, \beta, \rho$ and heston parameters $\nu, \kappa, \theta, \xi, \rho$?

How do they influence the smile; skewness, kurtosis, etc? And how are they related to one another, i.e., if I calibrate Heston to SABR for some fixed SABR-parameters, how will the estimated Heston parameters depend on the fixed SABR parameters?

Is there some good literature on the relationship between these two?

  • $\begingroup$ Add the equations for both stochastic processes to your question please. $\endgroup$ – will Apr 4 '17 at 20:40

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