On a positivity preserving numerical scheme for jump-extended CIR process: the alpha-stable case
On a positivity preserving numerical scheme for jump-extended CIR process: the alpha-stable case
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DOI：
10.1007/s10543-019-00753-8
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发表时间：
2019-04
影响因子：
1.5
通讯作者：
Libo Li;Daichi Taguchi
中科院分区：
文献类型：
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作者：
Libo Li;Daichi Taguchi
针对跳跃扩展的Cox-Ingersoll-Ross（CIR）过程提出了一个保正隐式Euler-Maruyama格式，其中跳跃由一个补偿谱正稳定过程控制.与已有的跳跃扩展CIR或常弹性方差过程的保正数值格式不同，本文所考虑的模型具有无穷的活性跳跃。在这个特定的模型中，我们计算了强收敛率并给出了一些数值说明。这种类型的跳跃扩展模型最初是在分支过程的背景下研究的，最近被引入到金融数学文献中，以模拟主权利率，电力和能源市场。
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-stable process for. 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.