Volterra Volatility Models: Option Pricing and Hedging
暫譯: Volterra 波動模型：選擇權定價與對沖

Di Nunno, Giulia, Mishura, Yuliya, Yurchenko-Tytarenko, Anton

Volterra Volatility Models: Option Pricing and Hedging
  • 出版商: Springer
  • 出版日期: 2026-08-05
  • 售價: $7,380
  • 貴賓價: 9.5 折 $7,011
  • 語言: 英文
  • 頁數: 342
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3032265754
  • ISBN-13: 9783032265753
  • 相關分類: Fintech

    • 海外代購書籍(需單獨結帳)

商品描述

Financial markets have extremely complex behavior that cannot be fully modeled using classical approaches. In particular, numerous empirical studies show that market volatility exhibits some form of long-range dependence and has time-varying Hölder regularity with prominent periods of "roughness" (i.e., of Hölder order ≈ 0.1). These two properties are far beyond the capabilities of classical Brownian diffusions and it is challenging to reproduce them simultaneously in one model. In the existing literature, the phenomenons of long-range dependence and roughness mentioned above are often addressed by using fractional Brownian motion. However, in this case, these two features turn out to be mutually exclusive and cannot be grasped simultaneously. Furthermore, existing stochastic models based on fractional Brownian motion pose additional challenges of the technical kind: they tend to produce prices with moment explosions (and hence are not applicable to pricing some widespread derivatives); they may have volatilities that hit zero (or even become negative) which results in problems with transitioning between physical and pricing measures; they often lack efficient numerical algorithms for derivative pricing, hedging, etc. In this book, we introduce a novel class of stochastic processes driven by general Hölder noises that allows for a very broad flexibility in the noises (to account for both roughness and long-range dependence simultaneously) and grasps the unconventional behavior of market volatility. We also present a variety of associated numerical methods and propose practically feasible algorithms for various applications, such as pricing of derivatives (including options with discontinuous payoffs) and quadratic hedging.

商品描述(中文翻譯)

金融市場的行為極為複雜，無法僅透過傳統方法完全建模。特別是，許多實證研究顯示市場波動性表現出某種形式的長期依賴性，並具有隨時間變化的Hölder正則性，並且在某些時期顯示出顯著的「粗糙性」（即Hölder階數約為0.1）。這兩個特性遠超過傳統布朗運動的能力，並且在一個模型中同時重現這些特性是具有挑戰性的。在現有文獻中，上述長期依賴性和粗糙性的現象通常是通過使用分數布朗運動來處理。然而，在這種情況下，這兩個特徵卻是互斥的，無法同時把握。此外，基於分數布朗運動的現有隨機模型還帶來了額外的技術挑戰：它們往往會產生具有瞬間爆炸的價格（因此不適用於某些廣泛使用的衍生品定價）；它們的波動性可能會降至零（甚至變為負值），這會導致在物理度量和定價度量之間轉換時出現問題；它們通常缺乏有效的數值算法來進行衍生品定價、對沖等。在本書中，我們介紹了一類由一般Hölder噪聲驅動的新型隨機過程，這類過程在噪聲方面提供了非常廣泛的靈活性（以同時考慮粗糙性和長期依賴性），並把握市場波動性的非常規行為。我們還提出了各種相關的數值方法，並為各種應用（如衍生品定價，包括具有不連續支付的選擇權和二次對沖）提出了實際可行的算法。

作者簡介

Giulia Di Nunno is a professor at the University of Oslo and an adjunct professor at Norwegian School of Economics (NHH). She received her PhD in mathematical statistics in 2003 from the University of Pavia. Her main research fields are stochastic analysis and control with financial modelling in view. She has worked in portfolio optimisation, risk evaluation, pricing and hedging, stochastic volatility modelling, and more recently, numerical methods and machine learning in finance. Di Nunno is the author and co-author of about 80 scientific works, including a monograph on Malliavin calculus for Levy Processes with Applications to Finance and she is an editor of various volumes, all published by Springer. She is active internationally within knowledge societies, research projects, and works as an editor for several leading journals. She has made significant contributions in promoting mathematics in education and research globally as well as promoting women in mathematics. She is also the recipient of the 2019 ICIAM Su Buchin Prize.

Yuliya Mishura received her PhD in probability and statistics from Kyiv University in 1978 and completed her postdoctoral degree in probability and statistics (Habilitation) in 1990. She is currently a professor of the Department of Probability, Statistics and Actuarial Mathematics at Taras Shevchenko National University of Kyiv. Having broad and varied scientific interests, she is the author/coauthor of more than 320 research papers and more than 20 books. Her research interests include theory and statistics of stochastic processes, stochastic differential equations, stochastic finance, stochastic analysis, functional limit theorems, entropies of probability distributions and stochastic systems and other applications of stochastics. She was the invited speaker of many international congresses and conferences and the organizer of a series of conferences. She is the Editor-in-Chief of the journal Theory of Probability and Mathematical Statistics, Coeditor-in-Chief of the journal Modern Stochastics: Theory and Applications and the associated editor of several journals. She was a team leader and participant in many international research projects.

Anton Yurchenko-Tytarenko completed his PhD at the Faculty of Mathematics and Natural Sciences, University of Oslo in 2022. He specializes in probability theory, statistics, and stochastic analysis, with research interests in financial modeling, particularly volatility, stochastic systems with memory, machine learning and numerical methods for random processes. He is currently a Senior Power Market Analyst at Statkraft Energi AS, where he focuses on modeling and forecasting prices of power market assets.

作者簡介(中文翻譯)

Giulia Di Nunno 是奧斯陸大學的教授及挪威經濟學院（NHH）的兼任教授。她於2003年在帕維亞大學獲得數學統計學博士學位。她的主要研究領域為隨機分析與控制，並以金融建模為重點。她曾從事投資組合優化、風險評估、定價與對沖、隨機波動性建模，以及最近的金融數值方法和機器學習。Di Nunno 是約80篇科學著作的作者和合著者，其中包括一本關於Levy過程的Malliavin微積分及其在金融中的應用的專著，並且她是多本由Springer出版的卷的編輯。她在國際知識社會、研究項目中活躍，並擔任多本領先期刊的編輯。她在全球推廣數學教育和研究方面做出了重要貢獻，並致力於促進女性在數學領域的發展。她也是2019年ICIAM Su Buchin獎的獲得者。

Yuliya Mishura 於1978年在基輔大學獲得概率與統計學博士學位，並於1990年完成概率與統計學的博士後學位（Habilitation）。她目前是基輔塔拉斯·舍甫琴科國立大學概率、統計與精算數學系的教授。她擁有廣泛而多樣的科學興趣，是320多篇研究論文和20多本書籍的作者/合著者。她的研究興趣包括隨機過程的理論與統計、隨機微分方程、隨機金融、隨機分析、函數極限定理、概率分佈的熵及隨機系統，以及隨機學的其他應用。她曾是多個國際大會和會議的受邀演講者，並組織了一系列會議。她是期刊《概率與數學統計理論》的主編、《現代隨機學：理論與應用》的共同主編，以及多本期刊的相關編輯。她曾是多個國際研究項目的團隊領導者和參與者。

Anton Yurchenko-Tytarenko 於2022年在奧斯陸大學數學與自然科學學院完成博士學位。他專注於概率論、統計學和隨機分析，研究興趣包括金融建模，特別是波動性、具有記憶的隨機系統、機器學習和隨機過程的數值方法。他目前是Statkraft Energi AS的高級電力市場分析師，專注於電力市場資產的建模和價格預測。

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