Back-of-the-envelope Swaptions in a Very Parsimonious Multi-Curve Interest Rate Model

We propose an elementary model in multi-curve setting that allows to price with simple exact closed formulas European swaptions. Swaptions can be both physical delivery and cash-settled ones. The proposed model is very parsimonious: it is a three-parameter multi-curve extension of the two-parameter J. Hull & A. White (1990) [Pricing interest-rate-derivative securities. Review of Financial Studies 3(4), 573-592] model. The model allows also to obtain simple formulas for all other plain vanilla Interest Rate derivatives and convexity adjustments. Calibration issues are discussed in detail.