# What interpolation methods are standard to use for interpolating on equity volatility surfaces?

The answer to this question (Volatility surface interpolation for Black-Scholes delta hedging) names Cubic Spline Interpolation and Guassian Process interpolation (is this exactly the same thing as Kriging?). What are the pros and cons of each method and are there different methods to consider than these two (apart from simple linear interpolation)?

Further, what are some good references for each method, are there any special considerations that should be taken when applying the methods to volatility surfaces specifically? Specifically for Gaussian Process interpolation as that seems to be far more complicated.

• I am not sure that this is what you are looking for, but I know that Andreasen & Huge have made a working paper about volatility interpolation for equities: ssrn.com/abstract=1694972 For yield curve construction Hagan & West discusses different interpolation methods: web.math.ku.dk/~rolf/HaganWest.pdf. However, I am not sure whether the discussion can be applied to the volatility surface as well. Jul 28 at 19:52
• Side note: any ivol interpolation method must respect the no-arbitrage restrictions in the price space, i.e. $dC/dK \leq 0$, $d^2C/dK^2\geq 0$, $dC/d\tau \geq 0$. Jul 29 at 4:22
• @mmencke Thanks, I will check that out. I think I'm looking for a more simpler discourse on standard practice however where as this seems to be more advances and focusing in on computational efficiency Jul 29 at 8:34