Why does everyone say $\rho$ is correlation in Surface SVI?

$w = \frac{\theta_t}{2}(1+\rho\psi(\theta_t)k + \sqrt{(\psi(\theta_t)k+\rho)^2+1-\rho^2})$, with $\rho \in [-1,1]$

This paper says it is proportional to the slope of smile at the ATM point.

This paper says it is the correlation between the stock price and its instantaneous volatility. What is the instantaneous volatility? I am confused because I am using surface SVI to model the implied volatility instead of stochastic volatility.

  • 4
    $\begingroup$ SVI can actually be derived as a limit of the Heston model. From that perspective you could say that $\rho$ is the correlation between the instantaneous vol and the spot. But in the context of IV interpolation I'd simply associate it with deviation from a perfectly symmetric smile as you can check yourself by plugging in $\rho = 0$ in the formula. $\endgroup$
    – Frido
    Mar 29 at 11:13


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.