Market Risk Analysis, Quantitative Methods in Finance 1st edition, Carol Alexander

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!

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.

I'm a Maple and occasional Mathematica programmer. I found this book to be of limited use, in no small part because of its insistence on using Excel as the instruction coding language.

Who is the book meant for? People in finance who are quants and who have to code surely would want some language that permits intensive use. Sorry but Excel doesn't cut it. Fine for those who use spreadsheets. But the intensive math described in the book seems better suited for another language. Yes you can map 1 language into another (basically it's 1 Turing machine into another). But there's a good reason why different languages co-exist, some are better suited for a given task.

It's confusingly written, with dense manipulations whose purpose is often obscure. The pendantic pedagogy here is very tiresome, after going through several hundred pages of it.

And the book uses Excel to demo the equations?! For serious analysis, providing code examples in Matlab, Mathematica or Maple would have been more useful.

A better alternative to this text would be if you search for the Frank Fabozzi series. He has authored or edited a bunch of financial texts that are far easier and more lucid reads.

Product Details :
Hardcover: 320 pages
Publisher: Wiley; Volume I edition (May 27, 2008)
Language: English
ISBN-10: 0470998008
ISBN-13: 978-0470998007
Product Dimensions: 6.9 x 1 x 9.8 inches

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Energy and Power Risk Management: New Developments in Modeling, Pricing, and Hedging 1st edition, Alexander Eydeland

The authors have written a very detailed, well structured text on the different models and developments in the power and fuel markets. It's a very complex, mathematical analysis of the different techniques being used, and the text may lose a number of readers in the overly rigorous formulations. For those involved in risk management, market modeling, or asset management, the book would be a good secondary or tertiary read after you've established a sound understanding of stochastic models and current hedging and pricing techniques in the marketplace. For the layman in the industry, the book will be far too heavy and not worth the read.

The management of risk in the context of energy or weather is quite different than in other contexts, due to the peculiarities of the data that occurs in energy prices. The high volatility of energy prices can range, as the authors of this book point out, between 50-100% for gas, to 100-500% for electricity. No doubt this kind of volatility, and other properties such as correlations and mean reversion, entails that some different mathematical strategies for modeling energy derivatives be devised. The authors give a good tour of some of these strategies, and anyone interested in energy derivatives will gain a lot of insight into their modeling when reading this book. Due to space constraints, only chapters 5 and 7, which this reviewer considered the most important of the book, will be reviewed here.

In chapter 5 the author presents techniques for energy modeling that go beyond the used of the convenience yield by using forward pricing techniques. The goal is to describe the dynamics of future contract prices that takes into account the correlations with other futures, and not on the price evolution of a single contract. Thus it is the `forward curve' that is relevant for obtaining a useable model for derivative cash flow. The HJM model is presented as one of these, with changes in the forward curve over a particular time interval represented as a linear combination of random perturbations. For energy markets, each perturbation is specified by a deterministic shape function multiplied by a Gaussian factor. The unobservability of the factors determining the forward curve evolution makes the use of historical data mandatory if the parameters are to be estimated. But lack of sufficient historical data and its nonstationarity complicate this estimation. The authors discuss the Schwartz-Smith multi-factor model as an example of a forward curve dynamics model and give some solutions. They then move on to a model that specifies the dynamics for only the contracts that are actually traded, which in the literature are called `market models.' The model they actually discuss is a multivariate geometric Brownian motion representation of the forward curve dynamics, where the volatility and drift functions are linear functions of the forward prices. The authors then derive the `discrete string models', where it is assumed that the number of factors is equal to the number of contracts, and the random factors are governed by ordinary Brownian motion. String models are represented as having the advantage of being able to directly observe the factors in the historical data. The authors apply string models to multi-commodity cases, and discuss an example for monthly forward prices. They show how to match the current forward curve, the option prices, and the correlation structure for this model.

The discussion in chapter 7 revolves around finding better models for the dynamics of power prices that capture the special properties of energy prices, such as mean reversion and seasonality, and the need for stable models. They therefore introduce `hybrid models', which they claim give a more natural representation of the dynamics of power prices, make use of nonprice forward-looking information, and can take the historical data on power prices and then extend it to information on fuel prices, outages, etc. The construction of these models is based on the use of nonlinear transformations on a collection of random variables. The random variables are essentially the system demand, natural gas and oil price, outages, emission prices, and weather at a particular time. The power price then can be written as a function of the dynamics of these factors, the latter written by the authors in terms of the corresponding tradables. Recognizing that hedging cannot be done on some of these factors, they adjust the power price formula so that the power tradables, i.e. the forwards and option prices, are exactly matched. This matching transformation is chosen so that if the forward contracts and options are priced using the adjusted formula, one recovers the exact current prices. The model, as the authors summarize it, is an attempt to explain the behavior of the tradables in terms of the evolution of the underlying factors and static adjustments to the terminal probability distribution. Historical information on the tradables and spot products is not used to calibrate the model, but it is used to validate the model. The authors distinguish between `reduced-form' hybrid models, where the transformation is calibrated from the historical prices, and `fundamental' hybrid models, where the transformation is calibrated from the market structure and is only tested on the historical prices. The authors discuss an example of a reduced-form hybrid model that is heavily parametrized, but has the advantage of using price data more efficiently. The rest of the chapter concentrates on fundamental hybrid models, with the author first discussing how power prices are formed in competitive markets. They consider a typical pool market, with the price determined via auction mechanisms. The authors then try to identify and characterize the underlying random variables that actually affect power prices. The time series for the price of power is written in terms of the demand using a `bid stack' function. The bid stack function is approximated by a `generation stack' that is found for a given time by sorting generation units by their generation costs. This approximation is checked by comparing the marginal generation costs generated by the generation stack with the distribution of power prices determined by the time series via the bid stack. There should be agreement in both approaches between the higher order moments. This comparison forms the basis of the authors' hybrid approach to modeling power prices. A transformation is found which relates the marginal generation costs to the distribution of power prices with the requirement that the prices of market instruments used for calibration are matched, and the higher moments are (approximately) preserved. The transformation is not unique, and in fact a family of transformations induced by the multiplication and stack scaling operators can be found.

Until now there were a handful of papers, precious few books, and mostly inside proprietary models and experience that dealt with the complex subject of power trading and all its flavors. This book provides a nice summary of many of the present issues. The treatment of the subject is somewhat mathematically rigorous, so the book might not be for traders as much as it is for quants or risk managers.

To me, the greatest strength of the book lies in its fairly detailed analysis of what DOESN'T work, i.e. why common models and methods from the financial and other commodity realms can not be successfully grafted onto the energy market without risking significant valuation and cash flow prediction errors. The hybrid model they formulate towards the end of the book is very similar to Skantze and Ilic (2001). The departure from most previous models is that they attempt to use the markets to formulate and calibrate the structure instead of relying too much on past historical price/load data, which without some empirical understanding of the underlying processes, is fraught with danger due to rapidly evolving nature of the power market (or at least once rapidly evolving--it seems to be a little static at the moment).

Some familiarity with the market and stochastic/statistical mathematics is assumed. References to specific topics and more in depth analysis of particular subjects are good. The authors have a grip on real-world trading, risk, and cashflow issues, which makes this a useful reference for just about anyone associated with those aspects of the power market. I recommend it.

Product Details :
Hardcover: 504 pages
Publisher: Wiley; 1 edition (December 30, 2002)
Language: English
ISBN-10: 0471104000
ISBN-13: 978-0471104001
Product Dimensions: 6.4 x 1.5 x 9.4 inches

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Stochastic Calculus and Financial Applications, Stochastic Modelling and Applied Probability, 1st edition, J. Michael Steele

MATHEMATICAL REVIEWS "…on the whole, the results are presented carefully and thoroughly, and I expect that readers will find that this combination of a careful development of stochastic calculus with many details and examples is very useful and will enable them to apply the whole theory confidently." SHORT BOOK REVIEWS "This is a world of 'lovely exercises' that are 'very good good for the soul', 'honest martingales', 'bedrock approximations', portfolios that are 'born to lose', 'intuitive but bogus arguments', and 'embarrassingly crude insights'. In short, this is a book on stochastic calculus of a different flavour. Intuition is not sacrificed for rigour nor rigour for intuition.The main results are reinforced with simple special cases, and only when the intuitive foundations are laid does the auhtor resort to the formalism of probability. The coverage is limited to the essentials but nevertheless includes topics that will catch the eye of experts (such as the wavelet construction of Brownian motion). This is one of the most interesting and easiest reads in the discipline; a gem of a book." JOURNAL OF THE AMERICAN STOCHASTIC ASSOCIATION "The book is indeed well written, with many insightful comments. I certainly would recommend it to students wishing to learn stochastic calculus and its applications to the Black-Sholes option-pricing theory…I thoroughly enjoyed reading this book. The author is to be complimented for his efforts in providing many useful insights behind the various theories. It is a superb introduction to stochastic calculus and Brownian motion…An interesting feature in this book is its coverage of partial differential equations." "It is clear that this is a fairly comprehensive introduction to the tools of (classical) mathematical finance. … the text has much to offer. … In addition, the writing style is refreshingly informal and makes a book about a rather technical subject surprisingly enjoyable to read. In short, despite the recent deluge of textbooks in this area, I know of no better book for self-study." (Christian Kleiber, Statistical Papers, Vol. 46 (2), 2005) "Steele’s book is a sophisticated introduction to stochastic calculus with applications from basic Black-Scholes theory. … I highly recommend the book. His style is wonderful, and concepts really build on one another. … it offers one of the most elegant treatments of the subject that I know of." (www.riskbook.com, May, 2006) "As is clear from the title of this book, it is concerned with applications of stochastic calculus to finance. … one naturally judges the book by three criteria: topic selection, organization, and exposition. In all three domains the book succeeds. The topics selected are rich enough … he or she will benefit from the book. … there are innovations as well … from the pedagogic standpoint." (Philip Protter, SIAM Review, Vol. 43 (4), 2001) "This book offers rich information and a mathematically honest treatment of stochastic calculus and of its use in the theory of finance … . The author gradually builds the reader’s ability to grasp stochastic concepts and techniques … . the author’s presentation of stochastic models in finance and economy is precise and extensive … . Each chapter is accompanied by a collection of rather challenging exercises … ." (EMS Newsletter, December, 2002) "The present book ‘is designed for students who want to develop professional skill in stochastic calculus and its application to problems in finance’. … the textbook … retains a lovely lecture style focusing basic ideas and not formalities and technical details of stochastic processes needed for finance. I can strongly recommend this book to students of mathematics and physics as well as non-experts in probability theory who are interested in stochastic finance." (H. –J. Girlich, Zeitschrift für Analysis und ihre Anwendungen, Vol. 21 (4), 2002) "The last few years have been a fertile period for books on stochastic calculus and its financial implications, but this one differs from the many mainstream treatments … . The style of the book creates the atmosphere of a lively lecture … . Each chapter ends with a section of carefully chosen exercises, preceded by some motivating remarks. … I really liked the book." (R. Grübel, Statistics & Decisions, Vol. 20 (4), 2002) "This book gives an introduction to stochastic calculus … with applications in mathematical finance. … As the preface says, ‘This is a text with an attitude, and it is designed to reflect, wherever possible and appropriate, a prejudice for the concrete over the abstract’. This is also reflected in the style of writing which is unusually lively for a mathematics book. … on the whole, the results are presented carefully and thoroughly … ." (Martin Schweizer, Zentralblatt MATH, Vol. 962, 2001) "This is a book on stochastic calculus of a different flavour. Intuition is not sacrificed for rigour nor rigour for intuition. The main results are reinforced with simple special cases … . This is one of the most interesting and easiest reads in the discipline; a gem of a book." (D. L. McLeish, Short Book Reviews, Vol. 21 (1), 2001)

Product Details :
Paperback: 312 pages
Publisher: Springer (December 1, 2010)
Language: English
ISBN-10: 1441928626
ISBN-13: 978-1441928627
Product Dimensions: 6.1 x 0.6 x 9.2 inches

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