A positivity preserving numerical scheme for the mean-reverting alpha-CEV process

Abstract

In this article, we present a method to construct a positivity preserving numerical scheme for both the jump-extended CEV process and jump-extended CIR process, whose jumps are governed by a (compensated) spectrally positive α-stable process with α ∈ (1, 2). The proposed scheme is obtained by making the diffusion coefficient partially implicit and then finding the appropriate adjustment factor. We show that the proposed scheme converges and theoretically achieves a strong convergence rate of at leastα , where the constant α− < α can be chosen arbitrarily close to α ∈ (1, 2). Finally, to support our result, we present some numerical simulations which suggest that the optimal rate of convergence is