Signature Methods in Finance: An Introduction with Computational Applications
暫譯: 金融中的簽名方法：計算應用入門

這本開放存取的書籍為快速成長的金融簽名方法領域提供了一個易於接觸的入門點。它是為早期職業研究者和具量化思維的從業者—量化分析師和應用研究者—撰寫的，旨在提供清晰、實用的介紹。書中突顯了最近的發展，並包含編碼範例，以幫助讀者在實踐中應用簽名方法。

從路徑的角度而非傳統的回報序列來建模金融市場的優勢，正逐漸獲得認可。簽名方法提供了隨機過程路徑的簡約描述，並通過簽名核開啟了機器學習與數學金融之間豐富而引人入勝的框架。

「在這段旅程中，我非常幸運能與傑出的合作者並肩工作，這本書美妙地反映了我們共同貢獻的豐富性—我對此深表感激。」—牛津大學、帝國學院的Terry Lyons教授及DataSig的首席研究員

「這本迷人的合集，獻給Terry Lyons，提供了對簽名方法及其多種用途的寶貴見解。」—Jim Gatheral，巴魯克學院的總統教授，2021年年度量化分析師

「這是對快速成長的簽名方法領域的及時且重要的貢獻，展示了這些強大理念的理論和應用。」—牛津大學的Ben Hambly教授

「這是一本關於簽名的令人印象深刻的書，收錄了該領域最傑出研究者的文章。從第一天起就是一本參考書。」—XTX Markets的聯合首席執行官Hans Buehler博士，2022年年度量化分析師

「這本書提供了對金融簽名方法的精湛闡述和發展。它簡潔、精確且可操作。對於任何對現代金融工程技術感興趣的人來說，都是一個極好的資源。」—ADIA全球研發負責人Alexander Lipton教授，ADIA Lab創始成員，2000年年度量化分析師及2021年買方年度量化分析師。

Christian Bayer is PI of the focus platform Quantitative analysis of stochastic and rough systems within the Weierstrass Institute (in Berlin). His main research interests are financial mathematics and stochastic numerics. One of his major research projects focuses on modelling stock indices like the S&P 500 index (SPX) consistently with respect to the implied volatility surface, and the volatility index (VIX). A specific issue is the behaviour of the implied volatility of options for very short maturities, which is largely believed to exhibit explosion in the form of a power law as maturity goes to zero. And these lead to rough volatility models. The theory of rough paths has many applications in machine learning. He is, in particular, interested in its applications to stochastic optimal control. He uses the path signature to derive efficient numerical approximation methods for stochastic optimal control problems, when the state process is not a Markov process.

Gonçalo dos Reis is an Associate Professor at the University of Edinburgh's School of Mathematics. He received his PhD in Mathematics from the Humboldt University of Berlin and works at the intersection of stochastic analysis, applied probability, and machine learning. His research combines theoretical developments with practical mathematics for industrial applications in finance, engineering, and energy systems. He serves on the editorial boards of several journals, including Energy and AI, and is regularly involved in the curation and dissemination of interdisciplinary research. In 2022, he received the University-wide Best PhD Supervisor of the Year prize in recognition of his mentorship and academic work. His research reflects a sustained engagement with interdisciplinary projects that address both academic and real-world challenges.

Blanka Horvath is an associate professor in mathematical and computational finance at the University of Oxford, an associate member of the Oxford-Man Institute and the 2024-25 Emmy Noether Fellow of the LMS. Her research is at the intersection of stochastic analysis and mathematical finance that includes option pricing, forecasting and simulation, with the use of asymptotic, - and numerical methods as well as machine learning techniques. In recent years, Blanka's research focus has been on rough path theory and signature methods, rough volatility models, and generative models. She is convinced of the value of an active dialogue between the financial sector's industry quants and academics. She has multiple ongoing research collaborations with industry partners on cutting-edge technological developments and regular engagements at industry conferences. Blanka is also the inaugural recipient of the Quant Rising Star Award 2020, and a member of the Rising Star Selection Panel ever since.

Harald Oberhauser is a Professor in the Mathematical Institute at the University of Oxford, a Tutorial Fellow at St. Hugh's College, and an associate member of the Oxford-Man Institute. He obtained his PhD from the Statslab in the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge. He held postdoctoral positions in Berlin and Oxford. Harald works on mathematics that allows to better understand, model and make inference about systems that evolve under the influence of randomness. He is especially interested in topics that connect recent progress in theoretical mathematics with real world applications.

Christian Bayer 是柏林魏爾斯特拉斯研究所（Weierstrass Institute）的隨機與粗糙系統定量分析重點平台的首席研究員。他的主要研究興趣包括金融數學和隨機數值分析。他的一個主要研究項目專注於對股票指數（如標準普爾500指數（S&P 500 index, SPX））進行建模，並與隱含波動率曲面（implied volatility surface）和波動率指數（volatility index, VIX）保持一致。一個特定的問題是，對於非常短期的期權，其隱含波動率的行為被廣泛認為在到期日接近零時會以冪律的形式爆炸。這些問題導致了粗糙波動率模型的產生。粗糙路徑理論在機器學習中有許多應用。他特別對其在隨機最優控制中的應用感興趣。當狀態過程不是馬可夫過程時，他使用路徑簽名（path signature）推導出高效的數值近似方法來解決隨機最優控制問題。

Gonçalo dos Reis 是愛丁堡大學數學學院的副教授。他在柏林洪堡大學獲得數學博士學位，並在隨機分析、應用概率和機器學習的交叉領域工作。他的研究結合了理論發展與實用數學，應用於金融、工程和能源系統的工業應用。他擔任多本期刊的編輯委員會成員，包括《Energy and AI》，並定期參與跨學科研究的策劃和傳播。2022年，他因其指導和學術工作獲得全校範圍內的《年度最佳博士生導師獎》。他的研究反映了對於解決學術和現實世界挑戰的跨學科項目的持續參與。

Blanka Horvath 是牛津大學數學與計算金融的副教授，牛津-曼研究所的副成員，以及2024-25年度LMS的艾米·諾特獎學者。她的研究位於隨機分析和數學金融的交叉點，包括期權定價、預測和模擬，並使用漸近方法、數值方法以及機器學習技術。近年來，Blanka的研究重點集中在粗糙路徑理論和簽名方法、粗糙波動率模型以及生成模型上。她堅信金融行業的量化分析師與學術界之間積極對話的價值。她與行業夥伴在尖端技術發展方面有多個持續的研究合作，並定期參加行業會議。Blanka也是2020年量化新星獎的首位獲得者，自那時起成為新星選拔小組的成員。

Harald Oberhauser 是牛津大學數學研究所的教授，聖休斯學院的導師成員，以及牛津-曼研究所的副成員。他在劍橋大學純數學與數學統計系的Statslab獲得博士學位，並在柏林和牛津擔任博士後職位。Harald的研究專注於數學，旨在更好地理解、建模和推斷在隨機影響下演變的系統。他特別對將理論數學的最新進展與現實世界應用相連接的主題感興趣。