Sandwiched Volterra Volatility 模型中的期权定价

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-09 DOI:10.1137/22m1521328

Giulia Di Nunno, Yuliya Mishura, Anton Yurchenko-Tytarenko

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引用次数: 0

摘要

SIAM 金融数学期刊》，第 15 卷第 3 期，第 824-882 页，2024 年 9 月。摘要.我们引入了一个由任意荷尔德连续高斯 Volterra 过程驱动的随机波动性金融市场新模型。该模型的显著特点是波动方程的形式，它确保了解被 "夹 "在事先选定的两个任意霍尔德连续函数之间。我们讨论了该市场上局部马氏计量的结构，研究了价格和波动率的可整性和马利亚文可微分性，并研究了相应概率规律的绝对连续性。此外，我们还利用马利亚文微积分开发了一种具有不连续报酬的期权定价算法。

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Option Pricing in Sandwiched Volterra Volatility Model

SIAM Journal on Financial Mathematics, Volume 15, Issue 3, Page 824-882, September 2024.
Abstract.We introduce a new model of financial market with stochastic volatility driven by an arbitrary Hölder continuous Gaussian Volterra process. The distinguishing feature of the model is the form of the volatility equation, which ensures that the solution is “sandwiched” between two arbitrary Hölder continuous functions chosen in advance. We discuss the structure of local martingale measures on this market, investigate integrability and Malliavin differentiability of prices and volatilities, and study absolute continuity of the corresponding probability laws. Additionally, we utilize Malliavin calculus to develop an algorithm of pricing options with discontinuous payoffs.

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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.