Positivity-preserving numerical scheme for the alpha-constant elasticity of variance process

In this article, we present a method for constructing a positivity-preserving numerical scheme for a jump-extended constant elasticity of variance (CEV) process, where jumps are governed by a spectrally positive α -stable process with α ∈ ( 1 , 2 ) . The numerical scheme is obtained by making the diffusion coefficient x γ , where γ ∈ ( 1 2 , 1 ) , partially implicit and then finding the appropriate adjustment factor. We show that for a sufficiently small step size, the proposed scheme converges and theoretically achieves a strong convergence rate of at least 1 2 ( α − 2 ∧ 1 α ∧ ρ ) , where ρ ∈ ( 1 2 , 1 ) is the Hölder exponent of the jump coefficient x ρ and the constant α − < α can be chosen as arbitrarily close to α ∈ ( 1 , 2 ) .