option pricing - Calculating implied volatility from moneyness/volatility values for date

For an option expiring at a particular date I have

Moneyness 0.4,0.7,0.85,0.95,1,1.05,1.15,1.3,2.5

Vol       0.105,0.075,0.045,0.045,0.202,0.045,0.045,0.075,0.085

How do I get the volatility for an option with a particular moneyness? Do I interpolate with an 8th degree polynomial? How would I then handle cases where moneyness is outside the range? Or do I need to do curve fitting?

Answer

The interpolation of the implied vol surface is no easy task unfortunately and it is subject of extensive research.

This is because you want the vol surface to have some nice characteristics, e.g.: be smooth, non arbitrable, etc.

Two approaches exist:

• Assuming a parametric form for the volatility surface and calibrating it on the quoted implied volatilies.


• Interpolation of the quoted implied volatilities. In this case, linear or polynomial might not be a good idea (not smooth), try cubic splines instead.

I will just add that everthing depends on what you want to do with this volatility afterwards.