Explicit Time Discretization Programming Approach to Risk Modelling

In this paper we formulate an explicit time discretization model for modeling risk by establishing an initial value problem as a function of time. The model is proved stable and the scaled-stability regions can encapsulated the volatile macroeconomic condition pertaining to financial risk. The model is extended to multistage schemes where we test for convergence under higherorder difference equations. Further, for addressing advection problems we have used Runge-Kutta method to propose a multistep model and have shown its stability patterns against general and absolute stability conditions. The paper also provides second-order and forth-order algorithm for computational programming of the models in practice. We conclude by stating that explicit time discretization models are stable and adequate for changing business environment.