Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model (Q634110)

The Ait-Sahalia-type model \(dx(t)=[\alpha_{-1}x(t)^{-1}-\alpha_0+\alpha_1x(t)-\alpha_2X(t)^r]dt+\sigma x(t)^{\rho} dw(t)\) with \(x(0)=x_0>0\), \(r>1\), \(\rho >1\), coming from the spot interest rate is considered. The existence and uniqueness of a global solution on \(t\in (0,\infty)\) of this Ito equation is established, and the main result is that the backward Euler-Maruyama discretization algorithm approximates strongly to the solution in the sense of \(p\)th moment uniformly on interval \([0,T]\). This result can be used to the Monte Carlo simulation.