Positivity-preserving truncated Euler-Maruyama method for generalised Ait-Sahalia-type interest model

The well-known Ait-Sahalia-type interest model, arising in mathematical finance, has some typical features: polynomial drift that blows up at the origin, highly nonlinear diffusion, and positive solution. The known explicit numerical methods including truncated/tamed Euler-Maruyama (EM) applied to it do not preserve its positivity. The main interest of this work is to investigate the numerical conservation of positivity of the solution of generalised Ait-Sahalia-type model. By modifying the truncated EM method to generate positive sequences of numerical approximations, we obtain the rate of convergence of the numerical algorithm not only at time T but also over the time interval [0, T]. Numerical experiments confirm the theoretical results.