On the Convergence Order of a Binary Tree Approximation of Symmetrized Diffusion Processes
On the Convergence Order of a Binary Tree Approximation of Symmetrized Diffusion Processes
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关于对称扩散过程二叉树逼近的收敛阶
DOI：
10.1016/j.matcom.2023.03.030
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发表时间：
2023
影响因子：
4.6
通讯作者：
Yuri Imamura
中科院分区：
文献类型：
--
作者：
Jiro Akahori;Jie Yen Fan;Yuri Imamura
障碍期权的价格通常是数值计算的。由于路径依赖性，这种数值逼近的收敛速度通常为1/2阶。本文证明了在一定的条件下，该算法的收敛阶为1。这证实了第三作者以前与其他人进行的数值分析。我们考虑的情况下，基本过程是一个布朗运动的漂移。障碍期权的价格与具有不连续漂移的“对称化”扩散的普通期权的价格一致。然后用马尔可夫链近似对称扩散，并计算相应的期权价格。这种近似的障碍选项被证明有一个收敛阶为1在一些温和的条件下的初始值的过程和支付函数。
The price of a barrier option is often computed numerically. Due to the path dependency, the convergence rate of such numerical approximation is generally of order 1/2. In this paper, we show that the convergence order can be achieved at 1 under certain condition. This confirms a numerical analysis done previously by the third author with others. We consider the case where the underlying process is a Brownian motion with drift. The price of a barrier option coincides with the price of a vanilla option of the “symmetrized” diffusion, which has a discontinuous drift. The symmetrized diffusion is then approximated by a Markov chain and the corresponding option price is calculated. This approximation to the barrier option is shown to have a convergence order of 1 under some mild condition on the initial value of the process and the payoff function.