Revisiting Stochastic Collocation with Exponential Splines for an Arbitrage-Free Interpolation of Option Prices

We revisit the stochastic collocation method using the exponential of a quadratic spline. In particular, we look in details whether it is more appropriate to fix the ordinates and optimize the abscissae of an interpolating spline or to fix the abscissae and optimize the parameters of a B-spline representation.