Before revision:  The normalized ksi-returns , correspondent to the kernel function in the found general solution and not dependent explicitly on time, were used for verification of the one-parameter model inherent efficiency, i.e. self-calibration using only historical volatility data. The model minimizes implied volatility bias (for 2004-2007 S& P100 index options) and theoretically yields skews correspondent to practical term structure for interest rate derivatives.
After revision:  The normalized ksi-returns , correspondent to the kernel function in the found general solution of backward drift-diffusion equation and normalized by theoretical diffusion coefficient, does not contain so-called "long tails" and unbiased for considered 2004-2007 S& P100 index options) and theoretically yields skews correspondent to practical term structure for interest rate derivatives.