对数调制粗糙随机波动模型

Risk Management eJournal Pub Date : 2020-08-07 DOI:10.2139/ssrn.3668973

Christian Bayer, Fabian A. Harang, P. Pigato

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引用次数: 10

摘要

本文提出了一类新的粗糙随机波动模型，该模型通过对数项调制幂律核来定义分数阶布朗运动(fBm)，使得核在Hurst指数$H$消失的极限情况下仍保持平方可积性。由此得到的对数调制分数布朗运动(log-fBm)即使在H = 0时也是一个连续的高斯过程。因此，所得到的超粗糙随机波动模型可以在整个范围内进行分析

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Log-Modulated Rough Stochastic Volatility Models

We propose a new class of rough stochastic volatility models obtained by modulating the power-law kernel defining the fractional Brownian motion (fBm) by a logarithmic term, such that the kernel retains square integrability even in the limit case of vanishing Hurst index $H$. The so-obtained log-modulated fractional Brownian motion (log-fBm) is a continuous Gaussian process even for $H = 0$. As a consequence, the resulting super-rough stochastic volatility models can be analysed over the whole range $0 \le H

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Risk Management eJournal

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