论文标题
使用随机网格
High order approximations of the Cox-Ingersoll-Ross process semigroup using random grids
论文作者
论文摘要
我们提出了通过使用Alfonsi和Bally（2021）（2021）对半群的最新技术获得的Cox-Ingersoll-Ross（CIR）过程的新的高阶近似值方案。该想法包括使用在不同随机网格上计算出的离散化方案的合适组合来增加收敛顺序。该技术加上Alfonsi（2010）针对CIR提出的第二阶方案，导致订单$ 2K $的较弱近似值，所有$ K \ in \ Mathbb {n}^*$ in \ Mathbb {n}^*$。尽管平方根的波动系数具有奇异性，但在对波动率参数的某些限制下，我们严格地显示了这种收敛顺序。我们从数值上说明了CIR过程和Heston随机波动率模型的这些近似值的收敛性，并显示它们给出的计算时间增长。
We present new high order approximations schemes for the Cox-Ingersoll-Ross (CIR) process that are obtained by using a recent technique developed by Alfonsi and Bally (2021) for the approximation of semigroups. The idea consists in using a suitable combination of discretization schemes calculated on different random grids to increase the order of convergence. This technique coupled with the second order scheme proposed by Alfonsi (2010) for the CIR leads to weak approximations of order $2k$, for all $k\in\mathbb{N}^*$. Despite the singularity of the square-root volatility coefficient, we show rigorously this order of convergence under some restrictions on the volatility parameters. We illustrate numerically the convergence of these approximations for the CIR process and for the Heston stochastic volatility model and show the computational time gain they give.
