Multi-Curves Framework with Stochastic Spread : A Coherent Approach to STIR Futures and Their Options

The development of the multi-curve framework has mainly concentrated on swaps and related products. By opposition, this contribution focuses on STIR futures and their options. They are analysed in a stochastic multiplicative spread multi-curve framework which allows a simultaneous modelling of the Ibor rates and of the cash-account required for futures with continuous margining. The framework proposes a coherent pricing of futures, swaps, cap/floor, and options on futures. The margined options on futures can be priced by reading the model quantities from the market with almost no calibration. In the final part of the note, we propose the pricing of a financial product which does not exists yet, betting that it will be proposed soon