# Using Cubic Spline with Vol Skew for Equity Options in R

I was recently attempting to replicate a part of the paper - DeMiguel, Plyakha, Uppal and Vilkov (2013), where they compute a model-free implied volatility (MFIV) quantity.

In the paper, the MFIV is computed as the root of the variance contract, which according to Bakshi et al. (2003), is the discretized sum of scaled prices of a continuum of call and put option prices. This continuum of call and put options are calculated with an inter and extrapolated volatility skew that is constructed with a cubic spline from existing implied volatilities of options that are currently traded in the market.

My question is, how can I not get negative implied volatilities from the cubic spline implementation? And is it correct to get negative implied volatilities in the first case?

• Hi and welcome. Could you post an example of your problem? If you have positive volatilities and interpolate between them, then the interpolated values should be positive too (also using cubic spline interpolation). So: no, your implied vols should always be positive ... Sep 20 at 11:55
• @RichiWa Thank you, I noticed that I was using OTM put and call-implied vols to inter and extrapolate a single volatility skew. When moving across K/S from left to right (put to call-implied volatility) there was a large deviation in IV. This resulted in the cubic spline being fitted very strangely, which led to negative IVs in the extrapolation region. Your answer gave me the confidence to check my modelling again :)
– Kai
Sep 20 at 12:33
• very good. Happy if that helped! Sep 21 at 13:06
• @RichiWa, can you turn your comment into an answer ? Sep 23 at 19:15
• @BobJansen I just did after your motivation:) Sep 23 at 20:04