Expand description
Bivariate thin-plate spline: the minimum-bending-energy surface
through scattered (x, y, z) points — the natural interpolant for an
irregular volatility quote grid (no rectangular layout required).
f(p) = a0 + a1 x + a2 y + sum_i w_i phi(|p - p_i|) with
phi(r) = r^2 ln r, coefficients from the standard augmented linear
system. A smoothing parameter >= 0 relaxes exact interpolation
toward a smoother least-squares surface (useful for noisy quotes).