Survival Analysis in Affine Setting Beatrice Acciaio ∗ and Elena Stanghellini † Preliminary and incomplete Abstract We study the survival probability of an homogeneous group of economic agents by adopting the reduced-form approach and assuming an affine evolution of the default intensities. We consider both the cases of continuous and discrete-times observations, and propose a modified likelihood function. We discuss the estimation of the parameters of interest and the forecast of default probabilities. 1 Setting We consider an homogeneous set of economic agents with the aim of studying their default probability. We observe them from a common starting point (say t = 0) and until their respective default or censuring times, either in a continuous way or in a discrete-time setting. We define the censure of an agent as the exit from the sample for any reason independent of the occurrence of default, which is bounded by a fixed future date (say t = T ), time horizon of our observations. For each firm i =1,...,N , denote τ i the default time, ξ i the censure time, and T i = τ i ∧ ξ i the first-exit time. Moreover, let f i (resp. F i , S i , h i ) be the density function (resp. cdf, survival function, hazard function) associated to τ i : F i (t)= P(τ i ≤ t)=  t 0 f i (u)du, S i (t)=1 − F i (t), h i (t)= f i (t) S i (t) . (1) * University of Perugia - Dep. Economy Finance and Statistics, Via A.Pascoli 20 - 06123 Perugia, and Vienna University of Technology - Dep. Financial and Actuarial Mathematics, Wiedner Haupt- strasse 8/105-1 A-1040 Vienna. email: beatrice.acciaio@stat.unipg.it, acciaio@fam.tuwien.ac.at. Financial support from the European Science Foundation (ESF) “Advanced Mathematical Methods for Finance” (AMaMeF) under the exchange grant 1192 is gratefully acknowledged. † University of Perugia - Dep. Economy Finance and Statistics, Via A.Pascoli 20 - 06123 Perugia. email: elena.stanghellini@stat.unipg.it 1