Dynamic Copula Methods in Finance

Balanced coverage of the methodology and theory of numerical methods in finance Numerical Methods in Finance bridges the gap between financial theory and computational practice while helping students and practitioners exploit MATLAB for financial applications. Paolo Brandimarte covers the basics of finance and numerical analysis and provides background material that suits the needs of students from both financial engineering and economics perspectives. Classical numerical analysis methods; optimization, including less familiar topics such as stochastic and integer programming; simulation, including low discrepancy sequences; and partial differential equations are covered in detail. Extensive illustrative examples of the application of all of these methodologies are also provided. The text is primarily focused on MATLAB-based application, but also includes descriptions of other readily available toolboxes that are relevant to finance. Helpful appendices on the basics of MATLAB and probability theory round out this balanced coverage. Accessible for students-yet still a useful reference for practitioners-Numerical Methods in Finance offers an expert introduction to powerful tools in finance.

This book is a detailed and step-by-step introduction to the mathematical foundations of ordinary and partial differential equations, their approximation by the finite difference method and applications to computational finance. The book is structured so that it can be read by beginners, novices and expert users. Part A Mathematical Foundation for One-Factor Problems Chapters 1 to 7 introduce the mathematical and numerical analysis concepts that are needed to understand the finite difference method and its application to computational finance. Part B Mathematical Foundation for Two-Factor Problems Chapters 8 to 13 discuss a number of rigorous mathematical techniques relating to elliptic and parabolic partial differential equations in two space variables. In particular, we develop strategies to preprocess and modify a PDE before we approximate it by the finite difference method, thus avoiding ad-hoc and heuristic tricks. Part C The Foundations of the Finite Difference Method (FDM) Chapters 14 to 17 introduce the mathematical background to the finite difference method for initial boundary value problems for parabolic PDEs. It encapsulates all the background information to construct stable and accurate finite difference schemes. Part D Advanced Finite Difference Schemes for Two-Factor Problems Chapters 18 to 22 introduce a number of modern finite difference methods to approximate the solution of two factor partial differential equations. This is the only book we know of that discusses these methods in any detail. Part E Test Cases in Computational Finance Chapters 23 to 26 are concerned with applications based on previous chapters. We discuss finite difference schemes for a wide range of one-factor and two-factor problems. This book is suitable as an entry-level introduction as well as a detailed treatment of modern methods as used by industry quants and MSc/MFE students in finance. The topics have applications to numerical analysis, science and engineering. More on computational finance and the author’s online courses, see www.datasim.nl.

Written by leading market risk academic, Professor Carol Alexander, Quantitative Methods in Finance forms part one of the Market Risk Analysis four volume set. Starting from the basics, this book helps readers to take the first step towards becoming a properly qualified financial risk manager and asset manager, roles that are currently in huge demand. Accessible to intelligent readers with a moderate understanding of mathematics at high school level or to anyone with a university degree in mathematics, physics or engineering, no prior knowledge of finance is necessary. Instead the emphasis is on understanding ideas rather than on mathematical rigour, meaning that this book offers a fast-track introduction to financial analysis for readers with some quantitative background, highlighting those areas of mathematics that are particularly relevant to solving problems in financial risk management and asset management. Unique to this book is a focus on both continuous and discrete time finance so that Quantitative Methods in Finance is not only about the application of mathematics to finance; it also explains, in very pedagogical terms, how the continuous time and discrete time finance disciplines meet, providing a comprehensive, highly accessible guide which will provide readers with the tools to start applying their knowledge immediately. All together, the Market Risk Analysis four volume set illustrates virtually every concept or formula with a practical, numerical example or a longer, empirical case study. Across all four volumes there are approximately 300 numerical and empirical examples, 400 graphs and figures and 30 case studies many of which are contained in interactive Excel spreadsheets available from the accompanying CD-ROM . Empirical examples and case studies specific to this volume include: Principal component analysis of European equity indices; Calibration of Student t distribution by maximum likelihood; Orthogonal regression and estimation of equity factor models; Simulations of geometric Brownian motion, and of correlated Student t variables; Pricing European and American options with binomial trees, and European options with the Black-Scholes-Merton formula; Cubic spline fitting of yields curves and implied volatilities; Solution of Markowitz problem with no short sales and other constraints; Calculation of risk adjusted performance metrics including generalised Sharpe ratio, omega and kappa indices.

The mathematical and statistical tools needed in the rapidly growing quantitative finance field With the rapid growth in quantitative finance, practitioners must achieve a high level of proficiency in math and statistics. Mathematical Methods and Statistical Tools for Finance, part of the Frank J. Fabozzi Series, has been created with this in mind. Designed to provide the tools needed to apply finance theory to real world financial markets, this book offers a wealth of insights and guidance in practical applications. It contains applications that are broader in scope from what is covered in a typical book on mathematical techniques. Most books focus almost exclusively on derivatives pricing, the applications in this book cover not only derivatives and asset pricing but also risk management—including credit risk management—and portfolio management. Includes an overview of the essential math and statistical skills required to succeed in quantitative finance Offers the basic mathematical concepts that apply to the field of quantitative finance, from sets and distances to functions and variables The book also includes information on calculus, matrix algebra, differential equations, stochastic integrals, and much more Written by Sergio Focardi, one of the world's leading authors in high-level finance Drawing on the author's perspectives as a practitioner and academic, each chapter of this book offers a solid foundation in the mathematical tools and techniques need to succeed in today's dynamic world of finance.

This book presents a cogent description of the main methodologies used in derivatives pricing. Starting with a summary of the elements of Stochastic Calculus, Quantitative Methods in Derivatives Pricing develops the fundamental tools of financial engineering, such as scenario generation, simulation for European instruments, simulation for American instruments, and finite differences in an intuitive and practical manner, with an abundance of practical examples and case studies. Intended primarily as an introductory graduate textbook in computational finance, this book will also serve as a reference for practitioners seeking basic information on alternative pricing methodologies. Domingo Tavella is President of Octanti Associates, a consulting firm in risk management and financial systems design. He is the founder and chief editor of the Journal of Computational Finance and has pioneered the application of advanced numerical techniques in pricing and risk analysis in the financial and insurance industries. Tavella coauthored Pricing Financial Instruments: The Finite Difference Method. He holds a PhD in aeronautical engineering from Stanford University and an MBA in finance from the University of California at Berkeley.

Quantitative Methods for Finance and Investments ensures that readers come away from reading it with a reasonable degree of comfort and proficiency in applying elementary mathematics to several types of financial analysis. All of the methodology in this book is geared toward the development, implementation, and analysis of financial models to solve financial problems.

Mathematical finance has grown into a huge area of research which requires a lot of care and a large number of sophisticated mathematical tools. Mathematically rigorous and yet accessible to advanced level practitioners and mathematicians alike, it considers various aspects of the application of statistical methods in finance and illustrates some of the many ways that statistical tools are used in financial applications. Financial Statistics and Mathematical Finance: Provides an introduction to the basics of financial statistics and mathematical finance. Explains the use and importance of statistical methods in econometrics and financial engineering. Illustrates the importance of derivatives and calculus to aid understanding in methods and results. Looks at advanced topics such as martingale theory, stochastic processes and stochastic integration. Features examples throughout to illustrate applications in mathematical and statistical finance. Is supported by an accompanying website featuring R code and data sets. Financial Statistics and Mathematical Finance introduces the financial methodology and the relevant mathematical tools in a style that is both mathematically rigorous and yet accessible to advanced level practitioners and mathematicians alike, both graduate students and researchers in statistics, finance, econometrics and business administration will benefit from this book.

Explore the foundations of modern finance with this intuitive mathematical guide In Mathematical Techniques in Finance: An Introduction , distinguished finance professional Amir Sadr delivers an essential and practical guide to the mathematical foundations of various areas of finance, including corporate finance, investments, risk management, and more. Readers will discover a wealth of accessible information that reveals the underpinnings of business and finance. You’ll learn about: Investment theory, including utility theory, mean-variance theory and asset allocation, and the Capital Asset Pricing Model Derivatives, including forwards, options, the random walk, and Brownian Motion Interest rate curves, including yield curves, interest rate swap curves, and interest rate derivativesComplete with math reviews, useful Excel functions, and a glossary of financial terms, Mathematical Techniques in Finance: An Introduction is required reading for students and professionals in finance.

Avoid downturn vulnerability by managing correlation dependency Asymmetric Dependence in Finance examines the risks and benefits of asset correlation, and provides effective strategies for more profitable portfolio management. Beginning with a thorough explanation of the extent and nature of asymmetric dependence in the financial markets, this book delves into the practical measures fund managers and investors can implement to boost fund performance. From managing asymmetric dependence using Copulas, to mitigating asymmetric dependence risk in real estate, credit and CTA markets, the discussion presents a coherent survey of the state-of-the-art tools available for measuring and managing this difficult but critical issue. Many funds suffered significant losses during recent downturns, despite having a seemingly well-diversified portfolio. Empirical evidence shows that the relation between assets is much richer than previously thought, and correlation between returns is dependent on the state of the market; this book explains this asymmetric dependence and provides authoritative guidance on mitigating the risks. Examine an options-based approach to limiting your portfolio's downside risk Manage asymmetric dependence in larger portfolios and alternate asset classes Get up to speed on alternative portfolio performance management methods Improve fund performance by applying appropriate models and quantitative techniques Correlations between assets increase markedly during market downturns, leading to diversification failure at the very moment it is needed most. The 2008 Global Financial Crisis and the 2006 hedge-fund crisis provide vivid examples, and many investors still bear the scars of heavy losses from their well-managed, well-diversified portfolios. Asymmetric Dependence in Finance shows you what went wrong, and how it can be corrected and managed before the next big threat using the latest methods and models from leading research in quantitative finance.