# Interpolation of SVI Implied Volatility in parameter space

I am currently working with a slice-wise SVI parametrisation of the implied volatility surface.

$$\sigma^2(x,t) = a_t + b_t (\rho_t (x - m_t) + \sqrt{(x - m_t)^2 + \theta^2})$$

Does anyone have experience with interpolation in parameter space? Is it possible to interpolate the implied volatility between maturities by interpolating the parameters and evaluating this "new" slice? Also is there a paper on the topic?

I have so far not been able to find one.

• I would suggest looking at Gatheral's original paper again. Then either perform the time interpolation in the jump wings parameter space or directly turn to something like SSVI and it's extensions for which the non arbitrage assumptions are built in by construction. Jul 10, 2019 at 6:49
• Thanks, I'll have another look at the alternatives in the paper. Jul 11, 2019 at 22:18