BOUNDARY PRESERVING EXPLICIT SCHEME FOR THE AIT-SAHALIA MODEL

We are interested in the numerical approximation of solutions of nonlinear stochastic differential equations, that appear in financial mathematics. Here, we study the A?? spacing diaeresis t-Sahalia model. We propose an explicit numerical scheme where we actually approximate the Lamperti transformation of the original stochastic differential equation and then transform back. The proposed method is domain preserving and is proven to converge strongly to the solution process with order at least 1 with no extra restrictions on the step-size Delta. Numerical experiments verify the theoretical results.