Multi-Curve Cheyette-Style Models with Lower Bounds on Tenor Basis Spreads

The modeling of tenor basis spreads is of central importance to CVA for tenor basis swaps. Such spreads are typically positive, suggesting a natural lower bound. We introduce a multi- curve Cheyette-style model with lower bounds enforced through level dependence in spread volatilities. The model is intuitive, easy to implement, and admits approximate swaption pricing formulae under affine specifications. We also discuss the importance of incorporating historical spread data into calibration criteria, and we formalize an according calibration strategy.