Applications of second order ornstein unlenbeck stochastic processes to credit risk modeling

Abstract

We consider applications of second order stochastic processes for analysis and forecasting credit loss. In contrast to the Vasicek model based on the one-dimensional Ornstein-Uhlenbeck stochastic differential equation driven by the Wiener process, we study two-dimensional analogues of Ornstein-Uhlenbeck processes driven by fractional Brownian motions. These processes are applied to extrapolation of macroeconomic factors for modeling account loss probability. Second order Ornstein-Uhlenbeck stochastic processes capture local behavior of economic factors providing more realistic tools in comparison with the first order Ornstein-Uhlenbeck processes. The obtained results are applied to different types of account loss rate models in frame of FASB’s Current Expected Credit Loss (CECL) and IASB’s International Financial Reporting Standards 9 (IFRS 9) rules.