Discrete-time Asset Pricing Models in Applied Stochastic Finance

While mainstream financial theories and applications assume that asset returns are normally distributed and individual preferences are quadratic, the overwhelming empirical evidence shows otherwise. Indeed, most of the asset returns exhibit “fat-tails” distributions and investors exhibit asymmetric preferences. These empirical findings lead to the development of a new area of research dedicated to the introduction of higher order moments in portfolio theory and asset pricing models. Multi-moment asset pricing is a revolutionary new way of modeling time series in finance which allows various degrees of long-term memory to be generated. It allows risk and prices of risk to vary through time enabling the accurate valuation of long-lived assets. This book presents the state-of-the art in multi-moment asset allocation and pricing models and provides many new developments in a single volume, collecting in a unified framework theoretical results and applications previously scattered throughout the financial literature. The topics covered in this comprehensive volume include: four-moment individual risk preferences, mathematics of the multi-moment efficient frontier, coherent asymmetric risks measures, hedge funds asset allocation under higher moments, time-varying specifications of (co)moments and multi-moment asset pricing models with homogeneous and heterogeneous agents. Written by leading academics, Multi-moment Asset Allocation and Pricing Models offers a unique opportunity to explore the latest findings in this new field of research.

This book provides a pedagogical examination of the way in which stochastic models are encountered in applied sciences and techniques such as physics, engineering, biology and genetics, economics and social sciences. It covers Markov and semi-Markov models, as well as their particular cases: Poisson, renewal processes, branching processes, Ehrenfest models, genetic models, optimal stopping, reliability, reservoir theory, storage models, and queuing systems. Given this comprehensive treatment of the subject, students and researchers in applied sciences, as well as anyone looking for an introduction to stochastic models, will find this title of invaluable use.

The credit derivatives market is booming and, for the first time, expanding into the banking sector which previously has had very little exposure to quantitative modeling. This phenomenon has forced a large number of professionals to confront this issue for the first time. Credit Derivatives Pricing Models provides an extremely comprehensive overview of the most current areas in credit risk modeling as applied to the pricing of credit derivatives. As one of the first books to uniquely focus on pricing, this title is also an excellent complement to other books on the application of credit derivatives. Based on proven techniques that have been tested time and again, this comprehensive resource provides readers with the knowledge and guidance to effectively use credit derivatives pricing models. Filled with relevant examples that are applied to real-world pricing problems, Credit Derivatives Pricing Models paves a clear path for a better understanding of this complex issue. Dr. Philipp J. Sch?nbucher is a professor at the Swiss Federal Institute of Technology (ETH), Zurich, and has degrees in mathematics from Oxford University and a PhD in economics from Bonn University. He has taught various training courses organized by ICM and CIFT, and lectured at risk conferences for practitioners on credit derivatives pricing, credit risk modeling, and implementation.

A fully updated edition of this key text on mixed models, focusing on applications in medical research The application of mixed models is an increasingly popular way of analysing medical data, particularly in the pharmaceutical industry. A mixed model allows the incorporation of both fixed and random variables within a statistical analysis, enabling efficient inferences and more information to be gained from the data. There have been many recent advances in mixed modelling, particularly regarding the software and applications. This third edition of Brown and Prescott’s groundbreaking text provides an update on the latest developments, and includes guidance on the use of current SAS techniques across a wide range of applications. Presents an overview of the theory and applications of mixed models in medical research, including the latest developments and new sections on incomplete block designs and the analysis of bilateral data. Easily accessible to practitioners in any area where mixed models are used, including medical statisticians and economists. Includes numerous examples using real data from medical and health research, and epidemiology, illustrated with SAS code and output. Features the new version of SAS, including new graphics for model diagnostics and the procedure PROC MCMC. Supported by a website featuring computer code, data sets, and further material. This third edition will appeal to applied statisticians working in medical research and the pharmaceutical industry, as well as teachers and students of statistics courses in mixed models. The book will also be of great value to a broad range of scientists, particularly those working in the medical and pharmaceutical areas.

A mixed model allows the incorporation of both fixed and random variables within a statistical analysis. This enables efficient inferences and more information to be gained from the data. The application of mixed models is an increasingly popular way of analysing medical data, particularly in the pharmaceutical industry. There have been many recent advances in mixed modelling, particularly regarding the software and applications. This new edition of a groundbreaking text discusses the latest developments, from updated SAS techniques to the increasingly wide range of applications. Presents an overview of the theory and applications of mixed models in medical research, including the latest developments and new sections on bioequivalence, cluster randomised trials and missing data. Easily accessible to practitioners in any area where mixed models are used, including medical statisticians and economists. Includes numerous examples using real data from medical and health research, and epidemiology, illustrated with SAS code and output. Features new version of SAS, including the procedure PROC GLIMMIX and an introduction to other available software. Supported by a website featuring computer code, data sets, and further material, available at: http://www.chs.med.ed.ac.uk/phs/mixed/. This much-anticipated second edition is ideal for applied statisticians working in medical research and the pharmaceutical industry, as well as teachers and students of statistics courses in mixed models. The text will also be of great value to a broad range of scientists, particularly those working the medical and pharmaceutical areas.

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.

Incorporates the many tools needed for modeling and pricing in finance and insurance Introductory Stochastic Analysis for Finance and Insurance introduces readers to the topics needed to master and use basic stochastic analysis techniques for mathematical finance. The author presents the theories of stochastic processes and stochastic calculus and provides the necessary tools for modeling and pricing in finance and insurance. Practical in focus, the book's emphasis is on application, intuition, and computation, rather than theory. Consequently, the text is of interest to graduate students, researchers, and practitioners interested in these areas. While the text is self-contained, an introductory course in probability theory is beneficial to prospective readers. This book evolved from the author's experience as an instructor and has been thoroughly classroom-tested. Following an introduction, the author sets forth the fundamental information and tools needed by researchers and practitioners working in the financial and insurance industries: * Overview of Probability Theory * Discrete-Time stochastic processes * Continuous-time stochastic processes * Stochastic calculus: basic topics The final two chapters, Stochastic Calculus: Advanced Topics and Applications in Insurance, are devoted to more advanced topics. Readers learn the Feynman-Kac formula, the Girsanov's theorem, and complex barrier hitting times distributions. Finally, readers discover how stochastic analysis and principles are applied in practice through two insurance examples: valuation of equity-linked annuities under a stochastic interest rate environment and calculation of reserves for universal life insurance. Throughout the text, figures and tables are used to help simplify complex theory and pro-cesses. An extensive bibliography opens up additional avenues of research to specialized topics. Ideal for upper-level undergraduate and graduate students, this text is recommended for one-semester courses in stochastic finance and calculus. It is also recommended as a study guide for professionals taking Causality Actuarial Society (CAS) and Society of Actuaries (SOA) actuarial examinations.

Optimal filtering applied to stationary and non-stationary signals provides the most efficient means of dealing with problems arising from the extraction of noise signals. Moreover, it is a fundamental feature in a range of applications, such as in navigation in aerospace and aeronautics, filter processing in the telecommunications industry, etc. This book provides a comprehensive overview of this area, discussing random and Gaussian vectors, outlining the results necessary for the creation of Wiener and adaptive filters used for stationary signals, as well as examining Kalman filters which are used in relation to non-stationary signals. Exercises with solutions feature in each chapter to demonstrate the practical application of these ideas using MATLAB.

Bayesian analysis of complex models based on stochastic processes has in recent years become a growing area. This book provides a unified treatment of Bayesian analysis of models based on stochastic processes, covering the main classes of stochastic processing including modeling, computational, inference, forecasting, decision making and important applied models. Key features: Explores Bayesian analysis of models based on stochastic processes, providing a unified treatment. Provides a thorough introduction for research students. Computational tools to deal with complex problems are illustrated along with real life case studies Looks at inference, prediction and decision making. Researchers, graduate and advanced undergraduate students interested in stochastic processes in fields such as statistics, operations research (OR), engineering, finance, economics, computer science and Bayesian analysis will benefit from reading this book. With numerous applications included, practitioners of OR, stochastic modelling and applied statistics will also find this book useful.

This book is entirely devoted to discrete time and provides a detailed introduction to the construction of the rigorous mathematical tools required for the evaluation of options in financial markets. Both theoretical and practical aspects are explored through multiple examples and exercises, for which complete solutions are provided. Particular attention is paid to the Cox, Ross and Rubinstein model in discrete time.

The book offers a combination of mathematical teaching and numerous exercises for wide appeal. It is a useful reference for students at the master’s or doctoral level who are specializing in applied mathematics or finance as well as teachers, researchers in the field of economics or actuarial science, or professionals working in the various financial sectors.

Martingales and Financial Mathematics in Discrete Time is also for anyone who may be interested in a rigorous and accessible mathematical construction of the tools and concepts used in financial mathematics, or in the application of the martingale theory in finance