A simple and general approach to fitting the discount curve under no-arbitrage constraints

•We describe a framework to fitting the discount curve under shape constraints.•The estimator is a monotonic penalized B-spline of arbitrary degree.•We estimate under the L1 and the L2 loss functions using two alternate penalties.•Empirical results show that the cubic estimators perform the best.•The penalty and the loss functions are less relevant. We suggest a simple and general approach to fitting the discount curve under no-arbitrage constraints based on a penalized shape-constrained B-spline. The approach accommodates B-splines of any order and fitting both under the L1 and the L2 loss functions. An application to US STRIPS data from 2001–2015 suggests that polynomial splines of order three and four are mandatory to obtain reasonable fits. The choice of the loss function appears to be less relevant.