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带跳随机波动率模型的高阶ADI分裂格式

陈迎姿1,2, 肖爱国2, 王晚生3   

  1. 1. 广东金融学院 金融数学与统计学院, 广州 510521;
    2. 湘潭大学数学与计算科学学院, 湘潭 411105;
    3. 上海师范大学数理学院, 上海 200234
  • 收稿日期:2021-12-04 出版日期:2022-11-14 发布日期:2022-11-08
  • 通讯作者: 王晚生,Email:w.s.wang@163.com.
  • 基金资助:
    国家自然科学基金青年项目(12101141)、国家自然科学基金项目(12271367,12071403,11771060)、上海市科技计划项目(20JC1414200)和上海市自然科学基金项目(20ZR1441200)资助.

陈迎姿, 肖爱国, 王晚生. 带跳随机波动率模型的高阶ADI分裂格式[J]. 计算数学, 2022, 44(4): 466-480.

Chen Yingzi, Xiao Aiguo, Wang Wansheng. HIGH ORDER ADI SPLITTING SCHEME FOR STOCHASTIC VOLATILITY MODEL WITH JUMP[J]. Mathematica Numerica Sinica, 2022, 44(4): 466-480.

HIGH ORDER ADI SPLITTING SCHEME FOR STOCHASTIC VOLATILITY MODEL WITH JUMP

Chen Yingzi1,2, Xiao Aiguo2, Wang Wansheng3   

  1. 1. School of financial mathematics and statistics, Guangdong University of Finance, Guangzhou 510521, China;
    2. School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China;
    3. College of Mathematics & Science, Shanghai Normal University, Shanghai 200234, China
  • Received:2021-12-04 Online:2022-11-14 Published:2022-11-08
针对带跳随机波动率模型满足的偏积分微分方程,提出一种新的高阶交替方向隐式(ADI)有限差分格式,该模型是一个具有混合导数和非常数系数的对流扩散型初边值问题.我们将不同的高阶空间离散与时间步ADI分裂格式相结合,得到了一种空间四阶精度、时间二阶精度的有效方法,并采用Fourier方法分析了高阶ADI格式的稳定性.最后,通过对欧式看跌期权定价模型进行数值实验证实了数值方法的高阶收敛性.
For the partial integro-differential equations satisfied by the stochastic volatility model with jump, a new high-order alternating direction implicit (ADI) finite difference scheme is proposed. The model is a convection diffusion type initial boundary value problem with mixed derivatives and non constant coefficients. We combine different high-order spatial discretization with the time-step ADI splitting scheme proposed by Hundsdorfer and Verwer, and obtain an effective method with fourth-order accuracy in space and second-order accuracy in time, and analyze the stability of high-order ADI scheme by Fourier method. Finally, the higher-order convergence of the numerical method is verified by numerical experiments on the European put option pricing model.

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