Product Description

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.

Product Details

• Amazon Sales Rank: #244313 in Books
• Published on: 2008-06-10
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 318 pages

From the Inside Flap
Market Risk Analysis is a series of four volumes:

Volume I: Quantitative Methods in Finance

Volume II: Practical Financial Econometrics

Volume III: Pricing, Hedging and Trading Financial Instruments

Volume IV: Value at Risk Models.

Although the four volumes are very much interlinked, each containing numerous cross-references to other volumes, they are written as self-contained texts.

Volume I covers the essential mathematical and financial background for subsequent volumes. There are six comprehensive chapters covering all the calculus, linear algebra, probability and statistics, numerical methods and portfolio mathematics that are necessary for market risk analysis. It is a complete and pedagogical introduction to quantitative methods applied to finance.

Volume II provides a detailed understanding of financial econometrics, with a unique focus on applications to asset pricing, fund management and market risk analysis. It covers equity factor models, including a detailed analysis of the Barra model and tracking error, principal component analysis, volatility and correlation, GARCH, cointegration, copulas, Markov switching, quantile regression, discrete choice models, non-linear regression, forecasting and model evaluation.

Volume III has five extensive chapters on the pricing, hedging and trading of bonds and swaps, futures and forwards, options and volatility, and detailed descriptions of mapping portfolios of these financial instruments to their risk factors. There are numerous examples, all coded in interactive Excel spreadsheets, including many pricing formulae for exotic options but excluding the calibration of stochastic volatility models, for which Matlab code is provided.

Volume IV builds on the three previous volumes to provide a comprehensive and detailed treatment of market VaR models. The exposition starts at an elementary level but, as in all the other volumes, the pedagogical approach accompanied by numerous interactive Excel spreadsheets allows readers to experience the application of parametric linear, historical simulation and Monte Carlo VaR models to increasingly complex portfolios. Starting with simple positions, readers are soon applying risk models to large international securities portfolios, commodity futures, path dependent options and much else. This rigorous treatment includes many new results and applications to regulatory and economic capital allocation, measurement of VaR model risk and stress testing.

Each volume is accompanied by a CD-ROM which features numerous interactive Excel spreadsheets that illustrate the vast majority of the problems and case studies in these texts. For further information see the accompanying CD-ROM.

From the Back Cover
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.

About the Author
Carol Alexander is a Professor of Risk Management at the ICMA Centre, University of Reading, and Chair of the Academic Advisory Council of the Professional Risk Manager’s International Association (PRMIA). She is the author of Market Models: A Guide to Financial Data Analysis(John Wiley & Sons Ltd, 2001) and has been editor and contributor of a very large number of books in finance and mathematics, including the multi-volume Professional Risk Manager’s Handbook(McGraw-Hill, 2008 and PRMIA Publications). Carol has published nearly 100 academic journal articles, book chapters and books, the majority of which focus on financial risk management and mathematical finance.

Professor Alexander is one of the world’s leading authorities on market risk analysis. For further details, see www.icmacentre.rdg.ac.uk/alexander

Customer Reviews

A God Sent
I have studied this book cover-to-cover, and I dare to say it is the best book from which to learn or review the math foundations used in quantitative finance (financial econometrics and derivatives pricing). I only have a degree of bachelor of science in computer science, with two years of analysis-lite calculus courses plus a one-semester calculus-based probability class, from the University of Toronto back in 1999, and I was able to understand most of this book. I also have very limited amount of time to study (basically just one half hour each week day on BART ride).

For someone with a similar background and time constraint as mine, Professor Alexander succinctly presents the foundational concepts of differentiation, integration, matrix algebra, multivariate probability, statistical inference, numerical methods, and portfolio theory. I had been searching for and could not find another book that covers so much ground in a single volume. Books like Mathematics for Economists (which I also highly recommend) do cover some of the maths, but do so from the perspectives of economics, not finance. Furthermore, they do not cover probability and statistics.

Contrary to what some other reviewers say, I think the use of Excel in the book is one of its best features. The company where I work uses SAS, S-PLUS, R, Matlab and Gauss, so I do have access to these tools. However, not everyone, especially those who are not working at a financial company, is so fortunate. Even though R is open source, it would add another learning curve on top of what is already a formidable challenge. Excel can be considered as the lowest common denominator, and if an algorithm can be implemented in it, you can bet that it can be ported to any other tool. Professor Alexander's avoidance of VBA is also greatly appreciated, as it would just add another layer of unnecessary complexity.

The only thing I miss from this book is more proofs or pointers to where we can find them. Don't get me wrong, this book is both practical and mathematically rigorous, and contains proofs or derivations for many theorems. However, probably due to the lack of space, a number of theorems are stated but not proved. For example, I would love to see more substantiation on why the t distributions are used for inferences on means and why the F distributions are for variance (section I.3.3.8). The standard I use to measure the clarity and completeness (in terms of proving from first principles) of other math books is Calculus by Professor Michael Spivak and Mathematical Statistics for Economics and Business by Professor Ron Mittelhammer (both of which I highly recommend; I am only half-way through the latter though). Having said that, Professor Alexander's book is probably as complete as anyone can make it with so few pages.

There are a number of gems of distilled insight throughout the book that I have not found elsewhere, such as the difference in notations of price between discrete and continuous times (section I.1.4.1) and the difference between "estimation" and "calibration" of models (p. 201). Professor Alexander's quality of being a great teacher and mentor shines through these examples. I wish I could be her student at the ICMA. In a way, I already am.

In summary, I cannot recommend this book highly enough for anyone who is starting to venture into the world of quantitative finance. I have already bought the rest of the volumes (save for volume IV, which is still unpublished) in the series, and I truly look forward to learning from them.

Congratulations, Professor Alexander, for writing this outstanding text.

Instant Classic
This is the 'Elements of Style' for Quantitative Finance: compact, style-setting, purposeful, and designed for the new learner. This book shouldn't be necessary: it reviews basic material that is elsewhere covered by bookshelves (library wings?) full of larger texts on the same topics. Instead, what's amazing is that it can replace an entire bookshelf of larger texts; it is that well-crafted.

The *style* is unique and ought to become the standard against which finance texts are judged. Unlike most finance texts, it does not meander. It is written by a teacher for new learners. Clearly, the author has put great care into the choices. Also clearly, the editing is superb. Like Hering Cheng, I have read it cover to cover. Nary a page is wasted. As finance texts goes, I find it simply delicious in elegance and economy of presentation. Served like a fine dish by a master chef who sweated every detail in the kitchen. The recipe may be lasagna (been there, done that) but still...the best lasagna.

The details, for example. Keywords emphasized in italics. Carefully considered hierarchical organization (e.g., I.3.3.2. It takes time to do this right). Language precision; e.g., a footnote that distinguishes analytic from closed-form, discussion on arithmetic/geometric Brownian motion that often stumps new learners but is often ignored in texts.

The book is informed by actual teaching, as it seems to anticipate many new learning hurdles. It is the first finance text I've read where the reader is not led down any big, blind alleys. Finance texts love to occasionally abandon new learners with an abrupt, intimidating formula. Prof. Alexander cares more than that. Important ideas concepts have concrete, actionable, workable examples. From start to finish, the text supports self-study (except, maybe just maybe, the matrices/eigenvalues may ask for a bit of outside help).

Regarding the criticism for using Excel: they are silly. Excel is the only correct choice for the audience. It is the only common denominator. Otherwise, the only way to meet the audience with examples is to show every example in three or four software code version. This is not necessary for an introduction, excel is the economical choice. And, btw, unlike most finance texts, the Excel worksheets are prepared with care; e.g., the regression XLS has embedded screenshots of the necessary add-in menus. Let us celebrate the lost art of attention to detail.

In regard to topics, book contains:

* Basic calculus and linear algebra (some of the building blocks that are so necessary to understanding complex instruments). The book comfortably uses matrices to go beyond two-asset portfolio examples.
* Probability and distributions. A good selection of distributions. But please note, however, the four sampling distributions (normal, student's t, F and chi-square) that are essential in Gujarati (for the FRM candidate) are only briefly listed.
* The best introduction to extreme value theory (EVT) that I've read. I have many texts on EVT, but this is where I would point a new learner.
* Actionable review of maximum likelihood estimation (i.e., accessible examples)
* Linear regression is standard but, to distinguish itself again, the book includes prototypical examples of their application in finance (oh, this is why we do linear regression in finance!)
* Tight intro to numerical methods
* Intro to portfolio theory includes utility theory (refreshingly, with examples)

I can't wait to start Volume II!

EXCELLENT AND BEST ALL ROUND QUANTITATIVE METHODS BOOK
Professor Alexander has done it once again with this wonderful gem of a book. This quantiative methods text no doubt will become standard issue in the industry. The book can assist risk managers, money manager, etc... a must for everyone working on Wall Street. This book should also help CFA students. CFA students would be wise to add this book to their collections. Congratulations on the 4 volume set and this book!

Greg N. Gregoriou, PhD
Professor of Finance
State University of New York (Plattsburgh)