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...

We introduce Negative Binomial Autoregressive (NBAR) processes for (univariate and bivariate) count time series. The univariate NBAR process is defined jointly with an underlying intensity process, which is autoregressive gamma. The resulting count process is Markov, with negative binomial...

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....

We introduce a general state-space (or latent factor) model for time series and panel data. The state process has a polynomial expansion based dynamics that can approximate any Markov dynamics arbitrarily well, and has a latent, endogenous switching regime interpretation. The resulting...

The Susceptible-Infected-Recovered (SIR) model is the cornerstone of epidemiological models. However, this specification depends on two parameters only, which implies a lack of flexibility and the difficulty to replicate the volatile reproduction numbers observed in practice. We extend the...

We introduce new semi-parametric models for the analysis of rates and proportions, such as proportions of default, (expected) loss-given-default and credit conversion factor encountered in credit risk analysis. These models are especially convenient for stress test exercises. We show that...

The increase of the expected lifetime, that is the longevity phenomenon, is accompanied by an increase of the number of seniors with a severe loss of autonomy. Because of the significant costs of long-term care (LTC) facilities, it is important to analyze the time spent in LTC state, as well as...

Whereas data on return volatilities are available for a large number of assets, this is less frequently the case of covolatilities. We introduce an approach based on static and dynamic Wishart models to solve this problem of missing data. We first discuss the identification of the parameter of...

The recursive prediction and filtering formulas of the Kalman filter are difficult to implementin nonlinear state space models. For Gaussian linear state space models, or for models with qualitativestate variables, the recursive formulas of the filter require the updating of a finite number...

By introducing a structure of the balance sheets of the banks, which takes into account their bilateral exposures in terms of stocks or lendings, we get a structural model for default analysis. This model allows distinguishing the exogenous and endogenous default dependence. We prove the...