The rough Hawkes Heston stochastic volatility model

IF 1.6 3区 经济学 Q3 BUSINESS, FINANCE
Alessandro Bondi, Sergio Pulido, Simone Scotti
{"title":"The rough Hawkes Heston stochastic volatility model","authors":"Alessandro Bondi,&nbsp;Sergio Pulido,&nbsp;Simone Scotti","doi":"10.1111/mafi.12432","DOIUrl":null,"url":null,"abstract":"<p>We study an extension of the Heston stochastic volatility model that incorporates rough volatility and jump clustering phenomena. In our model, named the rough Hawkes Heston stochastic volatility model, the spot variance is a rough Hawkes-type process proportional to the intensity process of the jump component appearing in the dynamics of the spot variance itself and the log returns. The model belongs to the class of affine Volterra models. In particular, the Fourier-Laplace transform of the log returns and the square of the volatility index can be computed explicitly in terms of solutions of deterministic Riccati-Volterra equations, which can be efficiently approximated using a multi-factor approximation technique. We calibrate a parsimonious specification of our model characterized by a power kernel and an exponential law for the jumps. We show that our parsimonious setup is able to simultaneously capture, with a high precision, the behavior of the implied volatility smile for both S&amp;P 500 and VIX options. In particular, we observe that in our setting the usual shift in the implied volatility of VIX options is explained by a very low value of the power in the kernel. Our findings demonstrate the relevance, under an affine framework, of rough volatility and self-exciting jumps in order to capture the joint evolution of the S&amp;P 500 and VIX.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Finance","FirstCategoryId":"96","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/mafi.12432","RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
引用次数: 0

Abstract

We study an extension of the Heston stochastic volatility model that incorporates rough volatility and jump clustering phenomena. In our model, named the rough Hawkes Heston stochastic volatility model, the spot variance is a rough Hawkes-type process proportional to the intensity process of the jump component appearing in the dynamics of the spot variance itself and the log returns. The model belongs to the class of affine Volterra models. In particular, the Fourier-Laplace transform of the log returns and the square of the volatility index can be computed explicitly in terms of solutions of deterministic Riccati-Volterra equations, which can be efficiently approximated using a multi-factor approximation technique. We calibrate a parsimonious specification of our model characterized by a power kernel and an exponential law for the jumps. We show that our parsimonious setup is able to simultaneously capture, with a high precision, the behavior of the implied volatility smile for both S&P 500 and VIX options. In particular, we observe that in our setting the usual shift in the implied volatility of VIX options is explained by a very low value of the power in the kernel. Our findings demonstrate the relevance, under an affine framework, of rough volatility and self-exciting jumps in order to capture the joint evolution of the S&P 500 and VIX.

粗略霍克斯-赫斯顿随机波动模型
我们研究了海斯顿随机波动率模型的扩展,该模型包含了粗略波动率和跳跃聚类现象。我们的模型被命名为粗糙霍克斯-赫斯顿随机波动率模型,在这个模型中,现货方差是一个粗糙霍克斯型过程,与现货方差本身和对数收益动态中出现的跳跃分量的强度过程成正比。该模型属于仿射 Volterra 模型。特别是,对数收益率的傅立叶-拉普拉斯变换和波动率指数的平方可以根据确定性里卡提-沃尔特拉方程的解来明确计算,而这些解可以使用多因子近似技术有效地近似。我们校准了以幂核和指数规律为特征的模型简约规范。我们的研究表明,我们的简化设置能够同时高精度地捕捉 S&P 500 和 VIX 期权的隐含波动率微笑行为。特别是,我们观察到,在我们的设置中,VIX 期权隐含波动率的通常变化是由核中非常低的幂值解释的。我们的研究结果表明,在仿射框架下,为了捕捉 S&P 500 指数和 VIX 指数的联合演化,粗略波动率和自激跳跃是相关的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Mathematical Finance
Mathematical Finance 数学-数学跨学科应用
CiteScore
4.10
自引率
6.20%
发文量
27
审稿时长
>12 weeks
期刊介绍: Mathematical Finance seeks to publish original research articles focused on the development and application of novel mathematical and statistical methods for the analysis of financial problems. The journal welcomes contributions on new statistical methods for the analysis of financial problems. Empirical results will be appropriate to the extent that they illustrate a statistical technique, validate a model or provide insight into a financial problem. Papers whose main contribution rests on empirical results derived with standard approaches will not be considered.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信