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.
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 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.
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.
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.
Textbook covering the basics of Fourier series, Fourier transforms and Laplace transforms.
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.
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.
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.
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.
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 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.
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
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
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
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.
An original and modern treatment of approximation theory for students in applied mathematics. Includes exercises, illustrations and Matlab code.
This textbook contains the fundamentals for an undergraduate course in mathematical finance aimed primarily at students of mathematics. Assuming only a basic knowledge of probability and calculus, the material is presented in a mathematically rigorous and complete way. The book covers the time value of money, including the time structure of interest rates, bonds and stock valuation; derivative securities (futures, options), modelling in discrete time, pricing and hedging, and many other core topics. With numerous examples, problems and exercises, this book is ideally suited for independent study.
The markets for electricity, gas and temperature have distinctive features, which provide the focus for countless studies. For instance, electricity and gas prices may soar several magnitudes above their normal levels within a short time due to imbalances in supply and demand, yielding what is known as spikes in the spot prices. The markets are also largely influenced by seasons, since power demand for heating and cooling varies over the year. The incompleteness of the markets, due to nonstorability of electricity and temperature as well as limited storage capacity of gas, makes spot-forward hedging impossible. Moreover, futures contracts are typically settled over a time period rather than at a fixed date. All these aspects of the markets create new challenges when analyzing price dynamics of spot, futures and other derivatives. This book provides a concise and rigorous treatment on the stochastic modeling of energy markets. OrnsteinOCoUhlenbeck processes are described as the basic modeling tool for spot price dynamics, where innovations are driven by time-inhomogeneous jump processes. Temperature futures are studied based on a continuous higher-order autoregressive model for the temperature dynamics. The theory presented here pays special attention to the seasonality of volatility and the Samuelson effect. Empirical studies using data from electricity, temperature and gas markets are given to link theory to practice. Sample Chapter(s). A Survey of Electricity and Related Markets (331 KB). Contents: A Survey of Electricity and Related Markets; Stochastic Analysis for Independent Increment Processes; Stochastic Models for the Energy Spot Price Dynamics; Pricing of Forwards and Swaps Based on the Spot Price; Applications to the Gas Markets; Modeling Forwards and Swaps Using the HeathOCoJarrowOCoMorton Approach; Constructing Smooth Forward Curves in Electricity Markets; Modeling of the Electricity Futures Market; Pricing and Hedging of Energy Options; Analysis of Temperature Derivatives. Readership: Researchers in energy and commodity markets, and mathematical finance.