A positivity preserving numerical scheme for the mean-reverting alpha-CEV process
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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 least 1/2(α_-/2∧1/α), 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 α_-/4.
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