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The present work is devoted to strong approximations of a generalizedAit-Sahalia model arising from mathematical finance. The numerical study of theconsidered model faces essential difficulties caused by a drift that blows upat the origin, highly nonlinear drift and diffusion coefficients andpositivity-preserving requirement. In this paper, a novel explicit Euler-typescheme is proposed, which is easily implementable and able to preservepositivity of the original model unconditionally, i.e., for any time step-sizeh>0. A mean-square convergence rate of order 0.5 is also obtained for theproposed scheme in both non-critical and general critical cases. Our work ismotivated by the need to justify the multi-level Monte Carlo (MLMC) simulationsfor the underlying model, where the rate of mean-square convergence is requiredand the preservation of positivity is desirable particularly for largediscretization time steps. To the best of our knowledge, this is the firstpaper to propose an unconditionally positivity preserving explicit scheme withorder 1/2 of mean-square convergence for the model. Numerical experiments arefinally provided to confirm the theoretical findings.

Unconditionally positivity-preserving explicit Euler-type schemes for a generalized Ait-Sahalia model