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In this paper we develop a framework for estimating Probability of Default(PD) based on stochastic models governing an appropriate asset value processes.In particular, we build upon a L\'evy-driven Ornstein-Uhlenbeck process andconsider a generalized model that incorporates multiple latent variablesaffecting the evolution of the process. We obtain an Integral Equation (IE)formulation for the corresponding PD as a function of the initial position ofthe asset value process and the time until maturity, from which we then provethat the PD function satisfies an appropriate Partial Integro-DifferentialEquation (PIDE). These representations allow us to show that appropriate weak(viscosity) as well as strong solutions exist, and develop subsequent numericalschemes for the estimation of the PD function. Such a framework is necessaryunder the newly introduced International Financial Reporting Standards (IFRS) 9regulation, which has imposed further requirements on the sophistication andrigor underlying credit modelling methodologies. We consider special cases ofthe generalized model that can be used for applications to credit riskmodelling and provide examples specific to provisioning under IFRS 9, and more.

Probability of Default modelling with L\'evy-driven Ornstein-Uhlenbeck processes and applications in credit risk under the IFRS 9