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Estimation in Conditionally Heteroscedastic Time Series Models
In his seminal 1982 paper, Robert F. Engle described a time series model with a time-varying volatility. Engle showed that this model, which he called ARCH (autoregressive conditionally heteroscedastic), is well-suited for the description of economic and financial price. Nowadays ARCH has been replaced by more general and more sophisticated models, such as GARCH (generalized autoregressive heteroscedastic). This monograph concentrates on mathematical statistical problems associated with fitting conditionally heteroscedastic time series models to data. This includes the classical statistical issues of consistency and limiting distribution of estimators. Particular attention is addressed to (quasi) maximum likelihood estimation and misspecified models, along to phenomena due to heavy-tailed innovations. The used methods are based on techniques applied to the analysis of stochastic recurrence equations. Proofs and arguments are given wherever possible in full mathematical rigour. Moreover, the theory is illustrated by examples and simulation studies.
Discrete Time Series, Processes, and Applications in Finance
Most financial and investment decisions are based on considerations of possible future changes and require forecasts on the evolution of the financial world. Time series and processes are the natural tools for describing the dynamic behavior of financial data, leading to the required forecasts. This book presents a survey of the empirical properties of financial time series, their descriptions by means of mathematical processes, and some implications for important financial applications used in many areas like risk evaluation, option pricing or portfolio construction. The statistical tools used to extract information from raw data are introduced. Extensive multiscale empirical statistics pro...
Risk Management
The use of derivative products in risk management has spread from commodities, stocks and fixed income items, to such virtual commodities as energy, weather and bandwidth. All this can give rise to so-called volatility and there has been a consequent development in formal risk management techniques to cover all types of risk: market, credit, liquidity, etc. One of these techniques, Value at Risk, was developed specifically to help manage market risk over short periods. Its success led, somewhat controversially, to its take up and extension to credit risk over longer time-scales. This extension, ultimately not successful, led to the collapse of a number of institutions. The present book, which was originally published in 2002, by some of the leading figures in risk management, examines the complex issues that concern the stability of the global financial system by presenting a mix of theory and practice.
The Theory of Credit Contracts
In this book Christian Prem features new innovations on several levels. On a conceptual level he presents a complete restructuring and modularisation of the field of lending theory. On a formal level he bestows great care on providing precise definitions and promotes notational standardisation. On a technical level the development of an algorithm to solve repayment games automatically is thoroughly documented. Eventually, new theoretic results on the performance of various credit schemes are established, the quality of existing lending schemes is scrutinised and new more efficient mechanisms are presented. The content therefore inspires theorists as well as it provides well-grounded advice to practitioners in the lending industry. Altogether this thesis is a major step towards improving the quality and applicability of lending theory.
An Introduction to Copulas
Copulas are functions that join multivariate distribution functions to their one-dimensional margins. The study of copulas and their role in statistics is a new but vigorously growing field. In this book the student or practitioner of statistics and probability will find discussions of the fundamental properties of copulas and some of their primary applications. The applications include the study of dependence and measures of association, and the construction of families of bivariate distributions. With nearly a hundred examples and over 150 exercises, this book is suitable as a text or for self-study. The only prerequisite is an upper level undergraduate course in probability and mathematical statistics, although some familiarity with nonparametric statistics would be useful. Knowledge of measure-theoretic probability is not required. Roger B. Nelsen is Professor of Mathematics at Lewis & Clark College in Portland, Oregon. He is also the author of "Proofs Without Words: Exercises in Visual Thinking," published by the Mathematical Association of America.
Risk and Liquidity
This book presents the Clarendon Lectures in Finance by one of the leading exponents of financial booms and crises. Hyun Song Shin's work has shed light on the global financial crisis and he has been a central figure in the policy debates. The paradox of the global financial crisis is that it erupted in an era when risk management was at the core of the management of the most sophisticated financial institutions. This book explains why. The severity of the crisis is explained by financial development that put marketable assets at the heart of the financial system, and the increased sophistication of financial institutions that held and traded the assets. Step by step, the lectures build an a...
Numerical Methods and Optimization in Finance
This book describes computational finance tools. It covers fundamental numerical analysis and computational techniques, such as option pricing, and gives special attention to simulation and optimization. Many chapters are organized as case studies around portfolio insurance and risk estimation problems. In particular, several chapters explain optimization heuristics and how to use them for portfolio selection and in calibration of estimation and option pricing models. Such practical examples allow readers to learn the steps for solving specific problems and apply these steps to others. At the same time, the applications are relevant enough to make the book a useful reference. Matlab and R sample code is provided in the text and can be downloaded from the book's website. Shows ways to build and implement tools that help test ideas Focuses on the application of heuristics; standard methods receive limited attention Presents as separate chapters problems from portfolio optimization, estimation of econometric models, and calibration of option pricing models
Risk and Portfolio Analysis
Investment and risk management problems are fundamental problems for financial institutions and involve both speculative and hedging decisions. A structured approach to these problems naturally leads one to the field of applied mathematics in order to translate subjective probability beliefs and attitudes towards risk and reward into actual decisions. In Risk and Portfolio Analysis the authors present sound principles and useful methods for making investment and risk management decisions in the presence of hedgeable and non-hedgeable risks using the simplest possible principles, methods, and models that still capture the essential features of the real-world problems. They use rigorous, yet e...
Psychiatric and Cognitive Disorders in Parkinson's Disease
A clear, comprehensive and practical account of the emotional and cognitive aspects of Parkinson's disease.
A Practical Introduction to Day Trading
Many individuals enter financial markets with the objective of earning a profit from capitalizing on price fluctuations. However, many of these new traders lose their money in attempting to do so. The reason for this is often because these new traders lack any fundamental understanding of financial markets, they cannot interpret any data, and they have no strategy for trading. Trading in markets is really about deploying strategies and managing risks. Indeed, successful traders are those who have strategies which they have proved to be consistent in granting them more financial gains than financial losses. The purpose of this book is to help a potentially uninformed retail trader or inquisitive reader understand more about financial markets, and assist them in gaining the technical skills required to profit from trading. It represents a beginner’s guide to trading, with a core focus on stocks and currencies.
