The ultra long run (ULR) discount rates are key inputs for valuing pension funds, life annuities, or firms with long run investments due to low carbon transition. However the corresponding zero-coupon bonds are only actively traded up to a last liquid point (LLP) such as 20 years, say. This...

Linear factor models, where the factors are affine processes, play a key role in Finance, since they allow for quasi-closed form expressions of the term structure of risks. We introduce the class of noncausal affine linear factor models by considering factors that are affine in reverse time....

This paper shows that the term structure of conditional, or predictive distributions allows for closed form expression in a large family of (possibly higher-order, or infinite order) thinning-based count processes such as INAR(p), INARCH(p), NBAR(p), and INGARCH(1,1). Very often, such predictive...