A Stable Time-Dependent Mesh Method for Generalized Credit Rating Migration Problem

The r-adaptive difference scheme is advanced in this article for solving the generalized credit rating migration model for arbitrary volatility with multiple terminal conditions. The r-adaptive moving mesh method defines the coordinate mapping from the physical to the computational domain and then uses piece-wise polynomials to approximate the physical coordinates. The central implicit semi-discretization scheme is imposed on space, and the backward Euler time marching scheme, coupled with several moving mesh partial differential equations, is used to achieve the numerical solution. The numerical operations are performed with several examples, and the obtained results are sufficiently accurate. The convergence of the proposed scheme is second-order, which is verified with the analysis. The article also investigates the stability and convergence of the adaptive mesh discretization scheme, which are not available in the literature; the convergence of the scheme is second-order in space and first-order in time.