The problems with generally used interpolation spaces

Volatility, as a crucial parameter for derivatives trading, is common to all asset classes. It is not, however, represented consistently, which precludes comprehensive cross-asset volatility transparency and management. As with many things, ‘the devil is in the detail' and something as seemingly simple as the choice of interpolation method can have a significant impact. Most ‘time interpolations' in ‘spaces' such as ‘strike' or ‘moneyness' are relatively meaningless as they ignore price dispersion over time implicit in volatility. A commonly used compromise is to adjust moneyness using ‘at-the-money' volatility (ATMV) interpolated at the square root of time. Using only ATMV ignores, however, the reality of smile. ‘Delta space' interpolation is consistent through time but is challenged by multiple definitions of delta. Even ignoring this challenge, the computational intensity of translating from smiled delta space back to strike or moneyness space results in less logical but simpler methods prevailing. Other methods, such as interpolating the parameters of a model, for example, SABR, between two dates are satisfactory but are exclusively linked to the given parametric method.