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Fourier-Malliavin Volatility Estimation

Author: Maria Elvira Mancino

Publisher: Springer

Published: 2017-03-01

Total Pages: 139

ISBN-13: 3319509691

This volume is a user-friendly presentation of the main theoretical properties of the Fourier-Malliavin volatility estimation, allowing the readers to experience the potential of the approach and its application in various financial settings. Readers are given examples and instruments to implement this methodology in various financial settings and applications of real-life data. A detailed bibliographic reference is included to permit an in-depth study.

Volatility Estimation Via Fourier Analysis

Author: Emilio Barucci

Publisher:

Published: 2000

Total Pages: 17

ISBN-13:

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Financial Mathematics, Volatility and Covariance Modelling

Author: Julien Chevallier

Publisher: Routledge

Published: 2019-06-28

Total Pages: 381

ISBN-13: 1351669095

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This book provides an up-to-date series of advanced chapters on applied financial econometric techniques pertaining the various fields of commodities finance, mathematics & stochastics, international macroeconomics and financial econometrics. Financial Mathematics, Volatility and Covariance Modelling: Volume 2 provides a key repository on the current state of knowledge, the latest debates and recent literature on financial mathematics, volatility and covariance modelling. The first section is devoted to mathematical finance, stochastic modelling and control optimization. Chapters explore the recent financial crisis, the increase of uncertainty and volatility, and propose an alternative approach to deal with these issues. The second section covers financial volatility and covariance modelling and explores proposals for dealing with recent developments in financial econometrics This book will be useful to students and researchers in applied econometrics; academics and students seeking convenient access to an unfamiliar area. It will also be of great interest established researchers seeking a single repository on the current state of knowledge, current debates and relevant literature.

Malliavin Calculus in Finance

Author: Elisa Alos

Publisher: CRC Press

Published: 2021-07-14

Total Pages: 350

ISBN-13: 1000403513

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Malliavin Calculus in Finance: Theory and Practice aims to introduce the study of stochastic volatility (SV) models via Malliavin Calculus. Malliavin calculus has had a profound impact on stochastic analysis. Originally motivated by the study of the existence of smooth densities of certain random variables, it has proved to be a useful tool in many other problems. In particular, it has found applications in quantitative finance, as in the computation of hedging strategies or the efficient estimation of the Greeks. The objective of this book is to offer a bridge between theory and practice. It shows that Malliavin calculus is an easy-to-apply tool that allows us to recover, unify, and generalize several previous results in the literature on stochastic volatility modeling related to the vanilla, the forward, and the VIX implied volatility surfaces. It can be applied to local, stochastic, and also to rough volatilities (driven by a fractional Brownian motion) leading to simple and explicit results. Features Intermediate-advanced level text on quantitative finance, oriented to practitioners with a basic background in stochastic analysis, which could also be useful for researchers and students in quantitative finance Includes examples on concrete models such as the Heston, the SABR and rough volatilities, as well as several numerical experiments and the corresponding Python scripts Covers applications on vanillas, forward start options, and options on the VIX. The book also has a Github repository with the Python library corresponding to the numerical examples in the text. The library has been implemented so that the users can re-use the numerical code for building their examples. The repository can be accessed here: https://bit.ly/2KNex2Y.

Multivariate Volatility Estimation with High Frequency Data Using Fourier Method

Author: Maria Elvira Mancino

Publisher:

Published: 2013

Total Pages: 53

ISBN-13:

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Availability of high frequency data has improved the capability of computing volatility in an efficient way. Nevertheless, measuring volatility/covariance from the observation of the asset price is challenging for two main reasons: observed asset prices are generally affected by noise microstructure effects and tick-by-tick returns are asynchronous across different assets. In this paper we review the definition and the statistical properties of the so called Fourier estimator of multivariate volatility, with particular focus on using high frequency data. Exploiting the fact that the method allows to compute both the integrated and the instantaneous volatility, we show how to obtain estimators of the volatility of the volatility and the leverage as well. Further, we study the performance of the estimator in forecasting and in terms of portfolio utility in the presence of microstructure noise contaminations.

Handbook of Modeling High-Frequency Data in Finance

Author: Frederi G. Viens

Publisher: John Wiley & Sons

Published: 2011-11-16

Total Pages: 468

ISBN-13: 1118204565

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CUTTING-EDGE DEVELOPMENTS IN HIGH-FREQUENCY FINANCIAL ECONOMETRICS In recent years, the availability of high-frequency data and advances in computing have allowed financial practitioners to design systems that can handle and analyze this information. Handbook of Modeling High-Frequency Data in Finance addresses the many theoretical and practical questions raised by the nature and intrinsic properties of this data. A one-stop compilation of empirical and analytical research, this handbook explores data sampled with high-frequency finance in financial engineering, statistics, and the modern financial business arena. Every chapter uses real-world examples to present new, original, and relevant topics that relate to newly evolving discoveries in high-frequency finance, such as: Designing new methodology to discover elasticity and plasticity of price evolution Constructing microstructure simulation models Calculation of option prices in the presence of jumps and transaction costs Using boosting for financial analysis and trading The handbook motivates practitioners to apply high-frequency finance to real-world situations by including exclusive topics such as risk measurement and management, UHF data, microstructure, dynamic multi-period optimization, mortgage data models, hybrid Monte Carlo, retirement, trading systems and forecasting, pricing, and boosting. The diverse topics and viewpoints presented in each chapter ensure that readers are supplied with a wide treatment of practical methods. Handbook of Modeling High-Frequency Data in Finance is an essential reference for academics and practitioners in finance, business, and econometrics who work with high-frequency data in their everyday work. It also serves as a supplement for risk management and high-frequency finance courses at the upper-undergraduate and graduate levels.

Ambit Stochastics

Author: Ole E. Barndorff-Nielsen

Publisher: Springer

Published: 2018-11-01

Total Pages: 402

ISBN-13: 3319941291

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Drawing on advanced probability theory, Ambit Stochastics is used to model stochastic processes which depend on both time and space. This monograph, the first on the subject, provides a reference for this burgeoning field, complete with the applications that have driven its development. Unique to Ambit Stochastics are ambit sets, which allow the delimitation of space-time to a zone of interest, and ambit fields, which are particularly well-adapted to modelling stochastic volatility or intermittency. These attributes lend themselves notably to applications in the statistical theory of turbulence and financial econometrics. In addition to the theory and applications of Ambit Stochastics, the book also contains new theory on the simulation of ambit fields and a comprehensive stochastic integration theory for Volterra processes in a non-semimartingale context. Written by pioneers in the subject, this book will appeal to researchers and graduate students interested in empirical stochastic modelling.

Stochastic Processes and Applications to Mathematical Finance

Author: Jiro Akahori

Publisher: World Scientific

Published: 2006

Total Pages: 228

ISBN-13: 9812565191

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Based around recent lectures given at the prestigious Ritsumeikan conference, the tutorial and expository articles contained in this volume are an essential guide for practitioners and graduates alike who use stochastic calculus in finance.Among the eminent contributors are Paul Malliavin and Shinzo Watanabe, pioneers of Malliavin Calculus. The coverage also includes a valuable review of current research on credit risks in a mathematically sophisticated way contrasting with existing economics-oriented articles.

Advances in Financial Planning and Forecasting (New Series) Vol．9

Author: Cheng F. Lee

Publisher: Center for PBBEFR & Ainosco Press

Published: 2018-01-01

Total Pages:

ISBN-13: 9866286746

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Advances in Financial Planning and Froecasting (New Series) is an annual publication designed to disseminate developments in the area of financial analysis, planning, and forecasting. The publication is a froum for statistical, quantitative, and accounting analyses of issues in financial analysis and planning in terms of finance, accounting, and economic data.

Noncausal Stochastic Calculus

Author: Shigeyoshi Ogawa

Publisher: Springer

Published: 2017-07-24

Total Pages: 216

ISBN-13: 4431565760

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This book presents an elementary introduction to the theory of noncausal stochastic calculus that arises as a natural alternative to the standard theory of stochastic calculus founded in 1944 by Professor Kiyoshi Itô. As is generally known, Itô Calculus is essentially based on the "hypothesis of causality", asking random functions to be adapted to a natural filtration generated by Brownian motion or more generally by square integrable martingale. The intention in this book is to establish a stochastic calculus that is free from this "hypothesis of causality". To be more precise, a noncausal theory of stochastic calculus is developed in this book, based on the noncausal integral introduced by the author in 1979. After studying basic properties of the noncausal stochastic integral, various concrete problems of noncausal nature are considered, mostly concerning stochastic functional equations such as SDE, SIE, SPDE, and others, to show not only the necessity of such theory of noncausal stochastic calculus but also its growing possibility as a tool for modeling and analysis in every domain of mathematical sciences. The reader may find there many open problems as well.