| 状态转换下欧式Merton跳扩散期权定价的拟合有限体积方法 |
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| 引用本文： | 甘小艇.状态转换下欧式Merton跳扩散期权定价的拟合有限体积方法[J].计算数学,2021,43(3):337-353. |
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| 作者姓名： | 甘小艇 |
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| 作者单位： | 1. 楚雄师范学院 数学与计算机科学学院, 楚雄 675000;2. 电子科技大学 数学科学学院, 成都 611731 |
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| 基金项目： | 国家自然科学基金（61463002），云南省地方本科高校（部分）基础研究联合专项面上项目（2019FH001-079）和云南省教育厅科学基金项目（2019J0369）资助. |
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| 摘 要： | 本文主要研究状态转换下欧式Merton跳扩散期权定价模型的拟合有限体积方法.针对该定价模型中的偏积分-微分方程，空间方向采用拟合有限体积方法离散，时间方向构造Crank-Nicolson格式.理论证明了数值格式的一致性、稳定性和单调性，因此收敛至原连续问题的解.数值实验验证了新方法的稳健性，有效性和收敛性.
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| 关 键 词： | 状态转换跳扩散模型 拟合有限体积法 Crank-Nicolson格式 数值实验 |
| 收稿时间： | 2019-08-16 |
FITTED FINITE VOLUME METHOD FOR PRICING EUROPEAN OPTIONS UNDER REGIME-SWITHCHING MERTON'S JUMP-DIFFUSION PROCESSES |
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| Gan Xiaoting.FITTED FINITE VOLUME METHOD FOR PRICING EUROPEAN OPTIONS UNDER REGIME-SWITHCHING MERTON'S JUMP-DIFFUSION PROCESSES[J].Mathematica Numerica Sinica,2021,43(3):337-353. |
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| Authors: | Gan Xiaoting |
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| Institution: | 1. School of Mathematics and Computer Science, Chuxiong Normal University, Chuxiong 675000, China;2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China |
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| Abstract: | In this paper, a fitted finite volume method for pricing European options under regime-switching Merton's jump-diffusion model is studied. For the partial integro-differential equations (PIDEs) of this pricing model, we develop a fitted finite volume method for the spatial discretization, coupled with the Crank-Nicolson time stepping scheme. Theoretical analyses have shown that the numerical scheme is consistent, stable and monotone, hence it ensures the convergence to the solution of continuous problem. Numerical experiments are presented to verify the robustness, effectiveness and convergence of the new method. |
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| Keywords: | Regime-switching jump-diffusion model Fitted finite volume method CrankNicolson scheme Numerical experiments |
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