Reconciling Rough Volatility with Jumps

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-06 DOI:10.1137/23m1558847

Eduardo Abi Jaber, Nathan De Carvalho

引用次数: 0

Abstract

SIAM Journal on Financial Mathematics, Volume 15, Issue 3, Page 785-823, September 2024.
Abstract.We reconcile rough volatility models and jump models using a class of reversionary Heston models with fast mean reversions and large vol-of-vols. Starting from hyper-rough Heston models with a Hurst index [math]-, we derive a Markovian approximating class of one-dimensional reversionary Heston-type models. Such proxies encode a trade-off between an exploding vol-of-vol and a fast mean-reversion speed controlled by a reversionary timescale [math] and an unconstrained parameter [math]. Sending [math] to 0 yields convergence of the reversionary Heston model toward different explicit asymptotic regimes based on the value of the parameter [math]. In particular, for [math], the reversionary Heston model converges to a class of Lévy jump processes of normal inverse Gaussian type. Numerical illustrations show that the reversionary Heston model is capable of generating at-the-money skews similar to the ones generated by rough, hyper-rough, and jump models.

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协调粗略波动与跳跃

SIAM 金融数学期刊》第 15 卷第 3 期第 785-823 页，2024 年 9 月。摘要.我们使用一类具有快速均值回归和大波动率的回归海斯顿模型来调和粗糙波动率模型和跳跃模型。从具有赫斯特指数[math]-的超粗糙赫斯顿模型出发，我们推导出一类马尔可夫近似的一维回归赫斯顿模型。这类近似模型在爆炸性的 Vol-of-vol 和快速的均值回归速度之间进行权衡，而快速均值回归速度由回归时标[math]和无约束参数[math]控制。将[math]设为 0 会导致回归海斯顿模型根据参数[math]的值向不同的显式渐近状态收敛。特别是，对于 [math]，回归海斯顿模型收敛于一类正态反高斯类型的莱维跳跃过程。数值说明显示，复归赫斯顿模型能够产生与粗糙模型、超粗糙模型和跳跃模型类似的价差偏斜。

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.