Exogenous shock and multifractal random walk
Exogenous shock and multifractal random walk
复制标题
外源冲击和多重分形随机游走
DOI：
10.1007/s40844-018-0106-9
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
K. & Maskawa
中科院分区：
文献类型：
--
作者：
Kuroda;K. & Maskawa
从离散时间模型出发，构造了多重分形随机游走的对数波动率过程作为标度极限，并考虑了外生冲击和波动率的松弛过程。在这个结构中，考虑到外生冲击的影响，我们考虑了一个模型的交易者与不同的投资时间范围进行交易。利用数学物理中发展起来的簇展开方法，得到了对数波动率过程尺度极限的收敛性。在此尺度限制下，我们证明了外生冲击后波动的松弛满足指数的逆幂律。
We construct a log-volatility process for Multifractal Random Walk from a discrete time model as a scale limit and consider an exogenous shock and the relaxation process of the volatility. In this construction, taking an effect of exogenous shock into account, we consider a model for trades transacted by traders with different investment time horizons. Using the method of cluster expansion developed in mathematical physics, we obtain the convergence of scale limit of log-volatility process. For this scale limit, we prove the relaxation of the volatility after exogenous shock is given by an inverse power lawwith exponent.