Search Results for "pricing-interest-rate-derivatives-a-fourier-transform-based-approach-a-fourier-tranform-based-approach-lecture-notes-in-economics-and-mathematical-systems"

Pricing Interest-Rate Derivatives

Pricing Interest-Rate Derivatives

A Fourier-Transform Based Approach

  • Author: Markus Bouziane
  • Publisher: Springer Science & Business Media
  • ISBN: 9783540770664
  • Category: Business & Economics
  • Page: 193
  • View: 5814
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The author derives an efficient and accurate pricing tool for interest-rate derivatives within a Fourier-transform based pricing approach, which is generally applicable to exponential-affine jump-diffusion models.

PDE and Martingale Methods in Option Pricing

PDE and Martingale Methods in Option Pricing

  • Author: Andrea Pascucci
  • Publisher: Springer Science & Business Media
  • ISBN: 9788847017818
  • Category: Mathematics
  • Page: 721
  • View: 2728
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This book offers an introduction to the mathematical, probabilistic and numerical methods used in the modern theory of option pricing. The text is designed for readers with a basic mathematical background. The first part contains a presentation of the arbitrage theory in discrete time. In the second part, the theories of stochastic calculus and parabolic PDEs are developed in detail and the classical arbitrage theory is analyzed in a Markovian setting by means of of PDEs techniques. After the martingale representation theorems and the Girsanov theory have been presented, arbitrage pricing is revisited in the martingale theory optics. General tools from PDE and martingale theories are also used in the analysis of volatility modeling. The book also contains an Introduction to Lévy processes and Malliavin calculus. The last part is devoted to the description of the numerical methods used in option pricing: Monte Carlo, binomial trees, finite differences and Fourier transform.

Spectral Analysis of Signals

Spectral Analysis of Signals

The Missing Data Case

  • Author: Yanwei Wang,Jian Li,Petre Stoica
  • Publisher: Morgan & Claypool Publishers
  • ISBN: 1598290010
  • Category: Technology & Engineering
  • Page: 102
  • View: 6313
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Spectral estimation is important in many fields including astronomy, meteorology, seismology, communications, economics, speech analysis, medical imaging, radar, sonar, and underwater acoustics. Most existing spectral estimation algorithms are devised for uniformly sampled complete-data sequences. However, the spectral estimation for data sequences with missing samples is also important in many applications ranging from astronomical time series analysis to synthetic aperture radar imaging with angular diversity. For spectral estimation in the missing-data case, the challenge is how to extend the existing spectral estimation techniques to deal with these missing-data samples. Recently, nonparametric adaptive filtering based techniques have been developed successfully for various missing-data problems. Collectively, these algorithms provide a comprehensive toolset for the missing-data problem based exclusively on the nonparametric adaptive filter-bank approaches, which are robust and accurate, and can provide high resolution and low sidelobes. In this book, we present these algorithms for both one-dimensional and two-dimensional spectral estimation problems.

Term-Structure Models

Term-Structure Models

A Graduate Course

  • Author: Damir Filipovic
  • Publisher: Springer Science & Business Media
  • ISBN: 3540680152
  • Category: Mathematics
  • Page: 256
  • View: 3513
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Changing interest rates constitute one of the major risk sources for banks, insurance companies, and other financial institutions. Modeling the term-structure movements of interest rates is a challenging task. This volume gives an introduction to the mathematics of term-structure models in continuous time. It includes practical aspects for fixed-income markets such as day-count conventions, duration of coupon-paying bonds and yield curve construction; arbitrage theory; short-rate models; the Heath-Jarrow-Morton methodology; consistent term-structure parametrizations; affine diffusion processes and option pricing with Fourier transform; LIBOR market models; and credit risk. The focus is on a mathematically straightforward but rigorous development of the theory. Students, researchers and practitioners will find this volume very useful. Each chapter ends with a set of exercises, that provides source for homework and exam questions. Readers are expected to be familiar with elementary Itô calculus, basic probability theory, and real and complex analysis.

Advanced Calculus

Advanced Calculus

Revised

  • Author: Lynn Harold Loomis,Shlomo Sternberg
  • Publisher: World Scientific Publishing Company
  • ISBN: 9814583952
  • Category: Mathematics
  • Page: 596
  • View: 4764
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An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

Interest-Rate Management

Interest-Rate Management

  • Author: Rudi Zagst
  • Publisher: Springer Science & Business Media
  • ISBN: 3662121069
  • Category: Business & Economics
  • Page: 341
  • View: 5411
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This book combines a rigorous overview of the mathematics of financial markets with an insight into the practical application of these models to the risk and portfolio management of interest-rate derivatives. It can also serve as a valuable textbook on financial markets for graduate and PhD students in mathematics. Interesting and comprehensive case studies illustrate the theoretical concepts.

Fourier Series and Integral Transforms

Fourier Series and Integral Transforms

  • Author: Allan Pinkus,Samy Zafrany
  • Publisher: Cambridge University Press
  • ISBN: 9780521597715
  • Category: Mathematics
  • Page: 189
  • View: 7867
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Textbook covering the basics of Fourier series, Fourier transforms and Laplace transforms.

Digital Transformation in Financial Services

Digital Transformation in Financial Services

  • Author: Claudio Scardovi
  • Publisher: Springer
  • ISBN: 3319669451
  • Category: Business & Economics
  • Page: 236
  • View: 8331
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This book analyzes the set of forces driving the global financial system toward a period of radical transformation and explores the transformational challenges that lie ahead for global and regional or local banks and other financial intermediaries. It is explained how these challenges derive from the newly emerging post-crisis structure of the market and from shadow and digital players across all banking operations. Detailed attention is focused on the impacts of digitalization on the main functions of the financial system, and particularly the banking sector. The author elaborates how an alternative model of banking will enable banks to predict, understand, navigate, and change the external ecosystem in which they compete. The five critical components of this model are data and information mastering; effective use of applied analytics; interconnectivity and “junction playing”; development of new business solutions; and trust and credibility assurance. The analysis is supported by a number of informative case studies. The book will be of interest especially to top and middle managers and employees of banks and financial institutions but also to FinTech players and their advisers and others.

Mathematical Techniques in Finance

Mathematical Techniques in Finance

Tools for Incomplete Markets

  • Author: Ales Cerný
  • Publisher: Princeton University Press
  • ISBN: 1400831482
  • Category: Business & Economics
  • Page: 416
  • View: 5280
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Originally published in 2003, Mathematical Techniques in Finance has become a standard textbook for master's-level finance courses containing a significant quantitative element while also being suitable for finance PhD students. This fully revised second edition continues to offer a carefully crafted blend of numerical applications and theoretical grounding in economics, finance, and mathematics, and provides plenty of opportunities for students to practice applied mathematics and cutting-edge finance. Ales Cerný mixes tools from calculus, linear algebra, probability theory, numerical mathematics, and programming to analyze in an accessible way some of the most intriguing problems in financial economics. The textbook is the perfect hands-on introduction to asset pricing, optimal portfolio selection, risk measurement, and investment evaluation. The new edition includes the most recent research in the area of incomplete markets and unhedgeable risks, adds a chapter on finite difference methods, and thoroughly updates all bibliographic references. Eighty figures, over seventy examples, twenty-five simple ready-to-run computer programs, and several spreadsheets enhance the learning experience. All computer codes have been rewritten using MATLAB and online supplementary materials have been completely updated. A standard textbook for graduate finance courses Introduction to asset pricing, portfolio selection, risk measurement, and investment evaluation Detailed examples and MATLAB codes integrated throughout the text Exercises and summaries of main points conclude each chapter

Derivatives Analytics with Python - Data Analytics, Models, Simulation, Calibration and Hedging + WS

Derivatives Analytics with Python - Data Analytics, Models, Simulation, Calibration and Hedging + WS

  • Author: Yves Hilpisch
  • Publisher: John Wiley & Sons
  • ISBN: 1119037999
  • Category: Business & Economics
  • Page: 352
  • View: 990
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Derivatives Analytics with Python: Data Analysis, Models, Simulation, Calibration and Hedging provides the necessary background information, theoretical foundations and numerical tools to implement a market-based valuation of stock index options. Topics are, amongst others, stylized facts of equity and options markets, risk-neutral valuation, Fourier transform methods, Monte Carlo simulation, model calibration, valuation and dynamic hedging. The financial models introduced in this book exhibit features like stochastic volatility, jump components and stochastic short rates. The approach is a practical one in that all important aspects are illustrated by a set of self-contained Python scripts. Benefits of Reading the Book: Data Analysis: Learn how to use Python for data and financial analysis. Reproduce major stylized facts of equity and options markets by yourself. Models: Learn risk-neutral pricing techniques from ground up, apply Fourier transform techniques to European options and advanced Monte Carlo pricing to American options. Simulation: Monte Carlo simulation is the most powerful and flexible numerical method for derivatives analytics. Simulate models with jumps, stochastic volatility and stochastic short rates. Calibration: Use global and local optimization techniques (incl. penalties) to calibrate advanced option pricing models to market quotes for options with different strikes and maturities. Hedging: Learn how to use advanced option pricing models in combination with advanced numerical methods to dynamically hedge American options. Python: All results, graphics, etc. presented are in general reproducible with the Python scripts accompanying the book. Benefit from more than 5,500 lines of code.

Analyzing Financial Data and Implementing Financial Models Using R

Analyzing Financial Data and Implementing Financial Models Using R

  • Author: Clifford Ang
  • Publisher: Springer
  • ISBN: 3319140752
  • Category: Business & Economics
  • Page: 351
  • View: 8402
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This book is a comprehensive introduction to financial modeling that teaches advanced undergraduate and graduate students in finance and economics how to use R to analyze financial data and implement financial models. This text will show students how to obtain publicly available data, manipulate such data, implement the models, and generate typical output expected for a particular analysis. This text aims to overcome several common obstacles in teaching financial modeling. First, most texts do not provide students with enough information to allow them to implement models from start to finish. In this book, we walk through each step in relatively more detail and show intermediate R output to help students make sure they are implementing the analyses correctly. Second, most books deal with sanitized or clean data that have been organized to suit a particular analysis. Consequently, many students do not know how to deal with real-world data or know how to apply simple data manipulation techniques to get the real-world data into a usable form. This book will expose students to the notion of data checking and make them aware of problems that exist when using real-world data. Third, most classes or texts use expensive commercial software or toolboxes. In this text, we use R to analyze financial data and implement models. R and the accompanying packages used in the text are freely available; therefore, any code or models we implement do not require any additional expenditure on the part of the student. Demonstrating rigorous techniques applied to real-world data, this text covers a wide spectrum of timely and practical issues in financial modeling, including return and risk measurement, portfolio management, options pricing, and fixed income analysis.

Real Options and Investment Incentives

Real Options and Investment Incentives

  • Author: Gunther Friedl
  • Publisher: Springer Science & Business Media
  • ISBN: 3540482687
  • Category: Business & Economics
  • Page: 119
  • View: 7221
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This work analyzes the problem of delegated decision-making within firms when investment projects are characterized by the possibility to make subsequent decisions after the initial investment decision has been made. By analyzing this question, the monograph combines and unifies two important lines of literature: on the one hand the literature on controlling investment decisions, on the other hand the investment valuation literature.

The Glaucoma Book

The Glaucoma Book

A Practical, Evidence-Based Approach to Patient Care

  • Author: Paul N. Schacknow,John R. Samples
  • Publisher: Springer Science & Business Media
  • ISBN: 0387767002
  • Category: Medical
  • Page: 1043
  • View: 7295
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Complete evidence-based medical and surgical management of glaucoma for both the general ophthalmologist in practice and residents The only book that covers the new generation of glaucoma procedures including trabectome, trabecular bypass and canaloplasty, by the experts who developed them Includes the latest laser treatments for glaucoma including micro diode and titanium saphire trabeculoplasty as well as laser from an external approach The most comprehensive coverage of the optic nerve and the importance of nerve fiber layer hemorrhage Provides an integrated approach to neovascular glaucoma merging treatment to the retina, with the use of new anti-VEGF drugs, tubes, and shunts to achieve the best outcome Integrates clinical science with basic science to outline the next steps in glaucoma therapy

Time Series Analysis and Its Applications

Time Series Analysis and Its Applications

With R Examples

  • Author: Robert H. Shumway,David S. Stoffer
  • Publisher: Springer
  • ISBN: 3319524526
  • Category: Mathematics
  • Page: 562
  • View: 1292
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The fourth edition of this popular graduate textbook, like its predecessors, presents a balanced and comprehensive treatment of both time and frequency domain methods with accompanying theory. Numerous examples using nontrivial data illustrate solutions to problems such as discovering natural and anthropogenic climate change, evaluating pain perception experiments using functional magnetic resonance imaging, and monitoring a nuclear test ban treaty. The book is designed as a textbook for graduate level students in the physical, biological, and social sciences and as a graduate level text in statistics. Some parts may also serve as an undergraduate introductory course. Theory and methodology are separated to allow presentations on different levels. In addition to coverage of classical methods of time series regression, ARIMA models, spectral analysis and state-space models, the text includes modern developments including categorical time series analysis, multivariate spectral methods, long memory series, nonlinear models, resampling techniques, GARCH models, ARMAX models, stochastic volatility, wavelets, and Markov chain Monte Carlo integration methods. This edition includes R code for each numerical example in addition to Appendix R, which provides a reference for the data sets and R scripts used in the text in addition to a tutorial on basic R commands and R time series. An additional file is available on the book’s website for download, making all the data sets and scripts easy to load into R.

FinTech in Germany

FinTech in Germany

  • Author: Gregor Dorfleitner,Lars Hornuf,Matthias Schmitt,Martina Weber
  • Publisher: Springer
  • ISBN: 331954666X
  • Category: Business & Economics
  • Page: 121
  • View: 9783
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This book focuses on market developments of crowdfunding, crowdinvesting, crowdlending, social trading, robo-advice, personal financial management, online payment and mobile payment in Germany. FinTech companies are an important driver of innovation in the financial industry. By making financial transactions more user-friendly and transparent, these firms potentially contribute to financial stability and economic growth. The authors define and categorize the different market segments that have emerged. They further provide an assessment of current market volumes and make forecasts for the next 5, 10 and 20 years. Particular attention is given to the empirical findings resulting from scholarly research. Furthermore, the authors evaluate how the German FinTech market ranks relative to international standards. This book will appeal to finance and entrepreneurship researchers as well as practitioners from banking and tech industries. “This book offers a fresh and fascinating look at the FinTech market. The authors provide a rigorous economic analysis of the FinTech market in Germany and offer many insights that are of interest to practitioners, academics, and policymakers alike.” –Professor Douglas Cumming, Schulich School of Business “Germany is one of the fastest growing FinTech markets in Europe. This book not only provides a comprehensive and systematic overview on the developments and actors, but undertakes a visionary outlook on the forthcoming decades based on scientific methods.” –Dr. Thomas Puschmann, Head of Swiss FinTech Innovation Lab

Frontiers in Quantitative Finance

Frontiers in Quantitative Finance

Volatility and Credit Risk Modeling

  • Author: Rama Cont
  • Publisher: John Wiley & Sons
  • ISBN: 9780470456804
  • Category: Business & Economics
  • Page: 300
  • View: 3516
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Introduction to Econophysics

Introduction to Econophysics

Correlations and Complexity in Finance

  • Author: Rosario N. Mantegna,H. Eugene Stanley
  • Publisher: Cambridge University Press
  • ISBN: 9781139431224
  • Category: Business & Economics
  • Page: N.A
  • View: 5194
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This book concerns the use of concepts from statistical physics in the description of financial systems. The authors illustrate the scaling concepts used in probability theory, critical phenomena, and fully developed turbulent fluids. These concepts are then applied to financial time series. The authors also present a stochastic model that displays several of the statistical properties observed in empirical data. Statistical physics concepts such as stochastic dynamics, short- and long-range correlations, self-similarity and scaling permit an understanding of the global behaviour of economic systems without first having to work out a detailed microscopic description of the system. Physicists will find the application of statistical physics concepts to economic systems interesting. Economists and workers in the financial world will find useful the presentation of empirical analysis methods and well-formulated theoretical tools that might help describe systems composed of a huge number of interacting subsystems.

Quantitative Finance and Risk Management

Quantitative Finance and Risk Management

A Physicist's Approach Second Edition

  • Author: Jan W Dash
  • Publisher: World Scientific Publishing Company
  • ISBN: 9814571253
  • Category: Business & Economics
  • Page: 1000
  • View: 1409
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Written by a physicist with extensive experience as a risk/finance quant, this book treats a wide variety of topics. Presenting the theory and practice of quantitative finance and risk, it delves into the "how to" and "what it's like" aspects not covered in textbooks or papers. A "Technical Index" indicates the mathematical level for each chapter. This second edition includes some new, expanded, and wide-ranging considerations for risk management: Climate Change and its long-term systemic risk; Markets in Crisis and the Reggeon Field Theory; "Smart Monte Carlo" and American Monte Carlo; Trend Risk — time scales and risk, the Macro–Micro model, singular spectrum analysis; credit risk: counterparty risk and issuer risk; stressed correlations — new techniques; and Psychology and option models. Solid risk management topics from the first edition and valid today are included: standard/advanced theory and practice in fixed income, equities, and FX; quantitative finance and risk management — traditional/exotic derivatives, fat tails, advanced stressed VAR, model risk, numerical techniques, deals/portfolios, systems, data, economic capital, and a function toolkit; risk lab — the nuts and bolts of risk management from the desk to the enterprise; case studies of deals; Feynman path integrals, Green functions, and options; and "Life as a Quant" — communication issues, sociology, stories, and advice.

40 Days of Dating

40 Days of Dating

An Experiment

  • Author: Timothy Goodman,Jessica Walsh
  • Publisher: ABRAMS
  • ISBN: 1613127154
  • Category: Self-Help
  • Page: 304
  • View: 4401
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“What would happen if Harry met Sally in the age of Tinder and Snapchat? . . . A field guide to Millennial dating in New York City” (New York Daily News). When New York–based graphic designers and long-time friends Timothy Goodman and Jessica Walsh found themselves single at the same time, they decided to try an experiment. The old adage says that it takes 40 days to change a habit—could the same be said for love? So they agreed to date each other for 40 days, record their experiences in questionnaires, photographs, videos, texts, and artworks, and post the material on a website they would create for this purpose. What began as a small experiment between two friends became an Internet sensation, drawing 5 million unique (and obsessed) visitors from around the globe to their site and their story. 40 Days of Dating: An Experiment is a beautifully designed, expanded look at the experiment and the results, including a great deal of material that never made it onto the site, such as who they were as friends and individuals before the 40 days and who they have become since.

Fourier Transform Methods in Finance

Fourier Transform Methods in Finance

  • Author: Umberto Cherubini,Giovanni Della Lunga,Sabrina Mulinacci,Pietro Rossi
  • Publisher: John Wiley & Sons
  • ISBN: 9780470684924
  • Category: Business & Economics
  • Page: 256
  • View: 6027
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In recent years, Fourier transform methods have emerged as one of the major methodologies for the evaluation of derivative contracts, largely due to the need to strike a balance between the extension of existing pricing models beyond the traditional Black-Scholes setting and a need to evaluate prices consistently with the market quotes. Fourier Transform Methods in Finance is a practical and accessible guide to pricing financial instruments using Fourier transform. Written by an experienced team of practitioners and academics, it covers Fourier pricing methods; the dynamics of asset prices; non stationary market dynamics; arbitrage free pricing; generalized functions and the Fourier transform method. Readers will learn how to: compute the Hilbert transform of the pricing kernel under a Fast Fourier Transform (FFT) technique characterise the price dynamics on a market in terms of the characteristic function, allowing for both diffusive processes and jumps apply the concept of characteristic function to non-stationary processes, in particular in the presence of stochastic volatility and more generally time change techniques perform a change of measure on the characteristic function in order to make the price process a martingale recover a general representation of the pricing kernel of the economy in terms of Hilbert transform using the theory of generalised functions apply the pricing formula to the most famous pricing models, with stochastic volatility and jumps. Junior and senior practitioners alike will benefit from this quick reference guide to state of the art models and market calibration techniques. Not only will it enable them to write an algorithm for option pricing using the most advanced models, calibrate a pricing model on options data, and extract the implied probability distribution in market data, they will also understand the most advanced models and techniques and discover how these techniques have been adjusted for applications in finance. ISBN 978-0-470-99400-9