粗糙波动模型的多因素近似

IF 1.4 4区经济学 Q3 BUSINESS, FINANCE

SIAM Journal on Financial Mathematics Pub Date : 2019-01-01 DOI:10.1137/18m1170236

Eduardo Abi Jaber, Omar El Euch

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引用次数: 6

摘要

粗糙波动率模型非常有吸引力，因为它们对历史波动率和隐含波动率都有很好的拟合。然而，由于波动过程的非马尔可夫性和非半鞅性，没有简单的方法来有效地模拟这些模型，这使得衍生品的风险管理成为一项复杂的任务。本文设计了可处理的多因素随机波动模型，该模型近似于粗糙波动模型，具有马尔可夫结构。此外，我们将我们的程序应用于粗略赫斯顿模型的具体情况。这反过来又使我们能够推导出一种数值方法来求解在这种情况下对数价格的特征函数中出现的分数阶里卡第方程。

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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Multifactor Approximation of Rough Volatility Models

Rough volatility models are very appealing because of their remarkable fit of both historical and implied volatilities. However, due to the non-Markovian and non-semimartingale nature of the volatility process, there is no simple way to simulate efficiently such models, which makes risk management of derivatives an intricate task. In this paper, we design tractable multi-factor stochastic volatility models approximating rough volatility models and enjoying a Markovian structure. Furthermore, we apply our procedure to the specific case of the rough Heston model. This in turn enables us to derive a numerical method for solving fractional Riccati equations appearing in the characteristic function of the log-price in this setting.

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来源期刊

SIAM Journal on Financial Mathematics MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

2.30

自引率

10.00%

发文量

期刊介绍： SIAM Journal on Financial Mathematics (SIFIN) addresses theoretical developments in financial mathematics as well as breakthroughs in the computational challenges they encompass. The journal provides a common platform for scholars interested in the mathematical theory of finance as well as practitioners interested in rigorous treatments of the scientific computational issues related to implementation. On the theoretical side, the journal publishes articles with demonstrable mathematical developments motivated by models of modern finance. On the computational side, it publishes articles introducing new methods and algorithms representing significant (as opposed to incremental) improvements on the existing state of affairs of modern numerical implementations of applied financial mathematics.