On a positivity preserving numerical scheme for jump-extended CIR process: the alpha-stable case. (English) Zbl 1480.65017
Summary: We propose a positivity preserving implicit Euler-Maruyama scheme for a jump-extended Cox-Ingersoll-Ross (CIR) process where the jumps are governed by a compensated spectrally positive \(\alpha\)-stable process for \(\alpha \in (1,2)\). Different to the existing positivity preserving numerical schemes for jump-extended CIR or constant elasticity variance process, the model considered here has infinite activity jumps. We calculate, in this specific model, the strong rate of convergence and give some numerical illustrations. Jump extended models of this type were initially studied in the context of branching processes and was recently introduced to the financial mathematics literature to model sovereign interest rates, power and energy markets.
MSC:
| 65C30 | Numerical solutions to stochastic differential and integral equations |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
Keywords:
implicit scheme; Euler-Maruyama scheme; alpha-CIR models; Lévy driven SDEs; Hölder continuous coefficients; spectrally positive Lévy processReferences:
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