Financial Engineering And Computation Principles Mathematics Algorithms

A comprehensive text and reference, first published in 2002, on the theory of financial engineering with numerous algorithms for pricing, risk management, and portfolio management.

This volume investigates algorithmic methods based on machine learning in order to design sequential investment strategies for financial markets. Such sequential investment strategies use information collected from the market's past and determine, at the beginning of a trading period, a portfolio; that is, a way to invest the currently available capital among the assets that are available for purchase or investment. The aim is to produce a self-contained text intended for a wide audience, including researchers and graduate students in computer science, finance, statistics, mathematics, and engineering. Contents:On the History of the Growth-Optimal Portfolio (M M Christensen)Empirical Log-Optimal Portfolio Selections: A Survey (L Györfi, Gy Ottucsák & A Urbán)Log-Optimal Portfolio-Selection Strategies with Proportional Transaction Costs (L Györfi & H Walk)Growth-Optimal Portfolio Selection with Short Selling and Leverage (M Horváth & A Urbán)Nonparametric Sequential Prediction of Stationary Time Series (L Györfi & G Ottuscák)Empirical Pricing American Put Options (L Györfi & A Telcs) Readership: Researchers, academics and graduate students in artificial intelligence/machine learning, and mathematical finance/quantitative finance. Keywords:Log-Optimal Portfolio;Growth-Optimal Portfolio;Sequential Investment Strategies for Financial MarketsKey Features:Covers machine learning algorithms for the aggregation of elementary investment strategiesHighlights multi-period and multi-asset tradingFocuses on nonparametric estimation of the underlying distributions in the market process

The book covers a wide range of topics, yet essential, in Computational Finance (CF), understood as a mix of Finance, Computational Statistics, and Mathematics of Finance. In that regard it is unique in its kind, for it touches upon the basic principles of all three main components of CF, with hands-on examples for programming models in R. Thus, the first chapter gives an introduction to the Principles of Corporate Finance: the markets of stock and options, valuation and economic theory, framed within Computation and Information Theory (e.g. the famous Efficient Market Hypothesis is stated in terms of computational complexity, a new perspective). Chapters 2 and 3 give the necessary tools of Statistics for analyzing financial time series, it also goes in depth into the concepts of correlation, causality and clustering. Chapters 4 and 5 review the most important discrete and continuous models for financial time series. Each model is provided with an example program in R. Chapter 6 covers the essentials of Technical Analysis (TA) and Fundamental Analysis. This chapter is suitable for people outside academics and into the world of financial investments, as a primer in the methods of charting and analysis of value for stocks, as it is done in the financial industry. Moreover, a mathematical foundation to the seemly ad-hoc methods of TA is given, and this is new in a presentation of TA. Chapter 7 reviews the most important heuristics for optimization: simulated annealing, genetic programming, and ant colonies (swarm intelligence) which is material to feed the computer savvy readers. Chapter 8 gives the basic principles of portfolio management, through the mean-variance model, and optimization under different constraints which is a topic of current research in computation, due to its complexity. One important aspect of this chapter is that it teaches how to use the powerful tools for portfolio analysis from the RMetrics R-package. Chapter 9 is a natural continuation of chapter 8 into the new area of research of online portfolio selection. The basic model of the universal portfolio of Cover and approximate methods to compute are also described.

Computational finance is an interdisciplinary field which joins financial mathematics, stochastics, numerics and scientific computing. Its task is to estimate as accurately and efficiently as possible the risks that financial instruments generate. This volume consists of a series of cutting-edge surveys of recent developments in the field written by leading international experts. These make the subject accessible to a wide readership in academia and financial businesses. The book consists of 13 chapters divided into 3 parts: foundations, algorithms and applications. Besides surveys of existing results, the book contains many new previously unpublished results.

Principles of Financial Engineering, Third Edition, is a highly acclaimed text on the fast-paced and complex subject of financial engineering. This updated edition describes the "engineering" elements of financial engineering instead of the mathematics underlying it. It shows how to use financial tools to accomplish a goal rather than describing the tools themselves. It lays emphasis on the engineering aspects of derivatives (how to create them) rather than their pricing (how they act) in relation to other instruments, the financial markets, and financial market practices. This volume explains ways to create financial tools and how the tools work together to achieve specific goals. Applications are illustrated using real-world examples. It presents three new chapters on financial engineering in topics ranging from commodity markets to financial engineering applications in hedge fund strategies, correlation swaps, structural models of default, capital structure arbitrage, contingent convertibles, and how to incorporate counterparty risk into derivatives pricing. Poised midway between intuition, actual events, and financial mathematics, this book can be used to solve problems in risk management, taxation, regulation, and above all, pricing. A solutions manual enhances the text by presenting additional cases and solutions to exercises. This latest edition of Principles of Financial Engineering is ideal for financial engineers, quantitative analysts in banks and investment houses, and other financial industry professionals. It is also highly recommended to graduate students in financial engineering and financial mathematics programs. The Third Edition presents three new chapters on financial engineering in commodity markets, financial engineering applications in hedge fund strategies, correlation swaps, structural models of default, capital structure arbitrage, contingent convertibles and how to incorporate counterparty risk into derivatives pricing, among other topics. Additions, clarifications, and illustrations throughout the volume show these instruments at work instead of explaining how they should act The solutions manual enhances the text by presenting additional cases and solutions to exercises

The disciplines of financial engineering and numerical computation differ greatly, however computational methods are used in a number of ways across the field of finance. It is the aim of this book to explain how such methods work in financial engineering; specifically the use of numerical methods as tools for computational finance. By concentrating on the field of option pricing, a core task of financial engineering and risk analysis, this book explores a wide range of computational tools in a coherent and focused manner and will be of use to the entire field of computational finance. Starting with an introductory chapter that presents the financial and stochastic background, the remainder of the book goes on to detail computational methods using both stochastic and deterministic approaches. Now in its fifth edition, Tools for Computational Finance has been significantly revised and contains: A new chapter on incomplete markets which links to new appendices on Viscosity solutions and the Dupire equation; Several new parts throughout the book such as that on the calculation of sensitivities (Sect. 3.7) and the introduction of penalty methods and their application to a two-factor model (Sect. 6.7) Additional material in the field of analytical methods including Kim’s integral representation and its computation Guidelines for comparing algorithms and judging their efficiency An extended chapter on finite elements that now includes a discussion of two-asset options Additional exercises, figures and references Written from the perspective of an applied mathematician, methods are introduced as tools within the book for immediate and straightforward application. A ‘learning by calculating’ approach is adopted throughout this book enabling readers to explore several areas of the financial world. Interdisciplinary in nature, this book will appeal to advanced undergraduate students in mathematics, engineering and other scientific disciplines as well as professionals in financial engineering.

Computational models and methods are central to the analysis of economic and financial decisions. Simulation and optimisation are widely used as tools of analysis, modelling and testing. The focus of this book is the development of computational methods and analytical models in financial engineering that rely on computation. The book contains eighteen chapters written by leading researchers in the area on portfolio optimization and option pricing; estimation and classification; banking; risk and macroeconomic modelling. It explores and brings together current research tools and will be of interest to researchers, analysts and practitioners in policy and investment decisions in economics and finance.