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Model of Continuous Random Cascade Processes in Financial Markets
Frontiers in Physics ( IF 3.1 ) Pub Date : 2020-10-29 , DOI: 10.3389/fphy.2020.565372
Jun-ichi Maskawa , Koji Kuroda

This article presents a continuous cascade model of volatility formulated as a stochastic differential equation. Two independent Brownian motions are introduced as random sources triggering the volatility cascade: one multiplicatively combines with volatility; the other does so additively. Assuming that the latter acts perturbatively on the system, the model parameters are estimated by the application to an actual stock price time series. Numerical calculation of the Fokker–Planck equation derived from the stochastic differential equation is conducted using the estimated values of parameters. The results reproduce the probability density function of the empirical volatility, the multifractality of the time series, and other empirical facts.



中文翻译:

金融市场中连续随机级联过程的模型

本文提出了一种由随机微分方程表示的连续波动率级联模型。引入了两个独立的布朗运动作为触发波动率级联的随机源:一个是乘以波动率,另一个是波动率。另一个这样做。假设后者对系统起微扰作用,则模型参数由应用程序估算到实际股价时间序列。使用参数的估计值对随机微分方程式进行的Fokker-Planck方程式进行数值计算。结果再现了经验波动率的概率密度函数,时间序列的多重分形以及其他经验事实。

更新日期:2020-11-27
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