SVI term structure

LesleYLyu · January 13th, 2015, 2:49 am

the raw SVI is only for one time slice, how to interpolate between different expiry? (free of calender arbitrage or not?)cheers

VivienB · January 13th, 2015, 3:53 pm

You can use this article (Andreasen, Huge, Volatility Interpolation) to interpolate IV without arbitrage.

LesleYLyu · January 14th, 2015, 1:20 am

Thanks VivienB. I went through this article several years ago when I was at school, but haven`t got time to implement. I ll give a try.But I was thinking this may be an approach totally different with SVI. We can either use a nonparametric way like this "volatility interpolation" article use, or we can try to fit a parametric model, like sabr sviSo I am thinking maybe there will exist some smart interpolation/extrapolation method consistent exactly with SVI. But anyway still appreciate your replyCheers

VivienB · January 14th, 2015, 8:58 am

I'm not sure there is (another) simple ways to interpolate IV between maturities, that is why the authors wrote this article.Moreover, the proposed methodology can be used with SVI fitting (and that's how I personally use it):Step 1 Fit SVI for each quoted maturities T_iStep 2 interpolate the IV between T_{i-1} and T_i using formula (6) of the articleNote that the SVI interpolated volatility is not necessarily arbitrage free at a given maturity, and the Andreasen Huge methodology allow to "fix" this problem.

LesleYLyu · January 15th, 2015, 1:48 am

brilliant! Thanks VivienB, I ll give a try.Personally I am implementing the model in "a class of term structures for SVI implied volatility" by Sebastien Gurrieri. I ll compare the results with the method you mentioned and keep updating this thread.Btw, you mentioned the SVI interpolated volatility is not arb-free, would you mind describe with more details? I know the raw SVI (only fit the smile/skew for a given maturity) is not arb-free with butterfly arbitrage(Axel Vogt counterexample).

VivienB · January 15th, 2015, 7:57 am

QuoteI know the raw SVI (only fit the smile/skew for a given maturity) is not arb-free with butterfly arbitrage(Axel Vogt counterexample).That's what I meant when I said that SVI vol is not arbitrage free.