Multiple curve modeling with CBI processes

In this talk, I will introduce a new approach for the multi-curve setting, whose main novelty consists in using continuous-state branching processes with immigration (CBI processes). This specific class of non-negative affine processes, due to its self-exciting behavior, enables the underlying model to capture the most striking characteristics of the post-crisis interest rate market, namely the presence of multiple yield curves as well as the strong fluctuations observed on the interbank rates, especially the persistence of unusually low interest rates. In particular, the monotonicity of Ibor-OIS spreads with respect to the corresponding tenor, reflecting the increased interbank risk on the market, will be recovered. Besides, an exact fit to the initially observed term structure will be possible by means of the flexibility of the proposed approach, and its analytical tractability will be expressed via closed-form valuation formulas for linear fixed-income products. Nonetheless, Fourier techniques will allow to efficiently price non-linear derivatives such as caps, floors along with swaptions. Finally, the empirical features of the present framework will be demonstrated through a parameter calibration procedure to market data.