Future feature: generating IV smile using delta instead of strike price

[tyrneh]

Summary:

• generating IV smile using delta instead of strike price has the advantage that it is more resilient against day-to-day changes in option prices

Source: (page 53 of link)
To convert a call price function into the relevant volatility
smile (and vice versa) involves transforming both axes in a
non-linear way. We convert option prices into implied
volatilities. The implied volatility is the volatility of the
underlying asset price implied by the Black-Scholes (1973)
model and is a non-linear transformation of the option price.
A conventional volatility smile plots implied volatility
against the strike price, but such smiles can vary in
smoothness from day to day, making consistent interpolation
problematic. We choose to interpolate implied volatilities
across deltas rather than strikes, as illustrated in Chart 5.
The delta of an option is the rate of change of the option
price with respect to the underlying asset price and is a
non-linear transformation of the strike price. These ‘delta
smiles’ have a more stable degree of smoothness from day
to day.
The interpolation across the delta smile as in Chart 5 is
done using a smoothing spline, which is a flexible
non-parametric technique. A smoothing spline is a
piecewise cubic polynomial, the smoothness of which is
controlled by a single parameter, the smoothness parameter.
Because we interpolate across delta space we can hold the
smoothing parameter constant from day to day. This
means that changes in pdfs from day to day reflect changes
in the underlying data, and not in the estimation
technique.