Convergence in probability of numerical solutions of a highly non-linear delayed stochastic interest rate model

Abstract

We study a delayed stochastic interest rate model with superlinearly growing coefficients and develop novel analytical tools to investigate the properties of both the true solution and its truncated Euler-Maruyama (TEM) approximation. In particular, we prove that the true solution converges in probability to the truncated EM solution as the step size approaches zero. Furthermore, we illustrate the theoretical findings through numerical experiments and validate the convergence results using an efficient Monte Carlo simulation framework for the valuation of relevant financial quantities.