Five stars for the intended audience, two stars for the likely holder (a theoretical approximation of the mathfin reader utility curve) give a three star average. Why? Practical utility skew is the operative third moment.

If you have no idea about what I just wrote, this book is not for you. If you do and it made you smile, keep reading.

In Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management authors Bouchaud and Potters place an additional veneer on their previous edition titled Theory of Financial Risks: From Statistical Physics to Risk Management, adding the sexy "Derivative Pricing" no doubt in a forgivable attempt to increase sales in this Googlfied world. But this is their failure. While the original edition was a fine, even respectable voice on bridging the knowledge of the intended audience of physicists-turned financial quant, this edition fails on the over covered subject of derivative pricing simply because it is not theoretical, but an empirical and technical review of historical data sets and assumptions and pricing techniques with critiques of the observed differences between theory and empirical results. Needless to say, this fails the smell test in physics, but in finance is as common as Shinola.

Sorry, but critiques of B-S assumptions and better curve fitting is technical, not theoretical. In other words, the theory of why third and fourth moments (skew and kurtosis) become operative and currently present arbitrage opportunities or risk management concerns is not adequately addressed, merely observed, expressed, and called attention to. Moreover, third and fourth moments are approached from a formulaic perspective intended primarily for risk managers and those seeking to make a buck (such as the authors themselves) and have only dangers emphasized. So formulas and expression yes, pure theory no.

Other reviewers have complained about a thematic Gauss-Levy versus Bachelier tone. Ho hum. For the day to day market maker (readers of Baird) such arguments pale in comparison to managing simply the delta of your book. For the physicist, the ghastly collection of noise and spikes that passes for a data set in finance will likely simply better be explained by long periods of madness followed by fleeting moments of clarity than any Procrustean attempt at better curve fitting informed for the empirical work of observing the data signals of a star's decay. Perhaps the only person Bouchaud and Potters's theoretical practical bridge tweaking would have assistance for would be the risk manager of the completely non-correlated short duration portion of the balance sheet of an international bank. Who also happened to be very powerful and have actual accurate real-time data and could implement these ideas. Scale? North of 8 billion before this is useful. Yep, in such a theta world Bachelier's technique rules. But we don't live in such a world yet, although risk managers everywhere delude themselves that they do, often armed with the likes of this book.

Let me hasten to add that Theory is not a bad thing, but its utility best serves the finmath community when it is clearly and explicitly so, without attempting techne and erte. This book is a forgivable beast with two backs, strongly skewed to a good critique of Theory and with fat tails of empiricism, and a bad attempt to be practical. This work therefore, again forgivably, is bound to disappoint practitioners. Joshi is your better bet.

Who is this book not for? Readers and users of Baird, Joshi and Hull and coding front-line quants and risk managers who live in a world of imperfect and delayed data sets will likely find this pointless academic obfuscation. Whom is this book for? I'm a finance guy, not a physicist, and so I read this book in a cyber book group with a theoretical physicist friend. He characterized the book as easy reading for him, but with little new to add that wasn't already known by the reasonably informed physicist turned finquant. His take was that it was a painfully obvious work, curiously passed off as original thinking when in reality it was simply a useful synthesis of common, though specialized knowledge. My take was it was tough sledding to get to obvious conclusions that anyone who has ever run an options book knows through painful experience or wise counsel. Elegantly expressed at a high level for a well-educated readership, but not exactly a holy grail. In other words, the juice wasn't worth the squeeze.

The major achievement of the book is concise presentation of the latest discoveries of the authors and their co-authors (Cont, Matacz). The discoveries are so significant that will lead in some 20 years to a Nobel Prize in Economics. They are: non-uniqueness of the option's price; role of kurtosis (the fourth moment of the price distribution) for volatility smile formula; a simple "square-root" formula for the FRC (forward rate curve of interest rate) accompanied by a simple explanation of a market mechanism behind it; deep "psychological" explanation (via Langevin equation) of the exponents 3-5 in the power-type tails of the price distributions; explanation of why VaR is systematically underestimated by Black-Scholes theory. However, all these discoveries require different mathematics and so far the authors are in search for the correct way to present them together coherently. There are several loose ends: many non-Gaussian approximations (which likely came from JPB's early works in physics and still beloved by him) without practical tools to estimate them; in the interesting chapter on random matrixes missing is a "market" explanation of the meaning of the eigenstates which stand behind 10% of "non-random" eigenvalues; absence of a serious discussion about exotic options points out to a difficulty to extend authors' methods toward more general options (while the regular PDE approach taken by other authors, like Wilmott, allows such an extension almost naturally).

This text has a nice discussion of Levy distributions and (important!) discusses why the central limit theorem does not apply to the tails of a distribution in the limit of many independent random events. An exponential distribution is given as an example how the CLT fails. I was first happy to see a chapter devoted to portfolio selection, but the chapter (like most of the book) is very difficult to follow (I gave up on that chapter, unhappily, because it looked interesting). The notation could have been better (to be quite honest, the notation is horrible), and the arguments (many of which are original) could have been made sharper and clearer. For my taste, too many arguments in the text rely on uncontrolled approximations, with Gaussian results as special limiting cases. The chapters on options are original, introducing their idea of history-dependent strategies (however, to get a strategy other than the delta-hedge does not not require history-dependence, CAPM is an example), but the predictions too often go in the direction of showing how Gaussian returns can be retrieved in some limit (I find this the opposite of convincing!). For an introduction to options, the 1973 Black-Scholes paper is still the best (aside from the wrong claim that CAPM and the delta-hedge yield the same results). The argument in the introduction in favor of 'randomness' as the origin of macroscopic law left me as cold as a cucumber. On page 4 a density is called 'invariant' under change of variable whereas 'scalar' is the correct word (a common error in many texts on relativity). The explanation of Ito calculus is inventive but inadequate (see instead Baxter and Rennie for a correct and readable treatment, one the forms the basis for new research on local volatility). Also, utlility is once mentioned but never criticized. Had the book been more pedagogically written then one could well have used it as an introductory text, given the nice choice of topics discussed.

Unfortunately, but not surprisingly, the previous reviewer prefered to remain anonymous. Otherwise, we would happily have argued with him privately. But his review contains so many erroneous and obnoxious statements that we feel we have to reply publicly, at least on the most important points.

a) After spending a full chapter (2) on empirical data and faithful models to describe them, we only price options using...the Brownian motion, says our reviewer (not even the Black-Scholes model, adds he). Well, either the reviewer has only casually browsed through our book, or this is total bad faith and disinformation. After discussing a general option pricing formula, we indeed illustrate it first (4.3.3) with the Black-Scholes model, then with Bachelier's (Brownian) model which, as we explain, is actually a better model for short term options. But the rest of the chapter is entirely devoted to non-Gaussian effects: a theory of the smile, its relation with kurtosis and long-ranged correlation in the volatility, and comparison with actual market smiles (4.3.4), and more importantly, the hedging strategies and residual risk (4.4), alternative hedging strategies for Value-at-Risk control (4.4.6), etc. The emphasis on risk, absent in the Black-Scholes world, is our main message, and partly justifies the title of our book.

b) "There is no statistical physics" in our book, moans the reviewer. Our aim was not to draw phoney analogies, but to present this field in the spirit of statistical physics, with what we feel is an interesting balance between intuition and rigour. (Many physicists feel stranded when reading standard mathematical finance books, where data is scarce, and rigour hides the inadequacies of the models). However, there are several genuine inputs from statistical physics, e.g. data processing, approximations, simple agent based models (2.8-9), functional derivatives to obtain optimal hedges (4.4), saddle point estimates of the Value at Risk for complex portfolios (5.4) and finally, Random Matrices that the reviewer finds unduly complex -- perhaps only because new to him. However, this is contained in "starred" section, indicating that it can be skipped at first reading, as many more advanced sections.

Two more details. We indeed sometimes consider independent random variables, sometimes only uncorrelated, hopefully not confusing the two. If the reviewer spotted incorrect statements, we would be grateful to him if we can correct them in further editions. Second, our book is not meant to provide ready to implement recipes but to present a different way of thinking about finance. Nevertheless, many of the ideas have already been implemented and are used by several (open minded?) financial institutions.

This book is a supposedly new approach to financial modeling from the viewpoint of "statistical physics". In fact, it is far from being that. First, there is little or no content really related to statistical physics in it. Apart from the fact that random variables and stochastic processes are also used in physics, the only feature in common between statistical physics and this book is some notational similarities and a lack of rigour which, justified in the case where it is supplemented by physical intuition, leads here to numerous mistakes and sloppy reasoning.

The title, while promising, is quite arrogant: not only there is no "theory of financial risks" in the book but many of the main issues of risk management are not even mentioned: Value at Risk receives less than a page at the end, while hedging of exotic options is not even an issue.

Also, while the first part of the book insists on choosing the correct distribution for price returns, the chapter on options exclusively gives computations for the case of ...Brownian motion (not even exponential Brownian motion)! One is left wondering whether these fancy models presented in the first part were worth mentioning?

Another point is the readership of this book: given the notational complexity of the book and the analogies with physics, only a PhD in theoretical physics can possibly find this book readable. In fact, a finance student will find it too light on the finance side while a math-minded student will find it too sloppy and imprecise.

The surprisingly low level of mathematical rigour - one confuses regularly "uncorrelated" with "independence"- is nevertheless accompanied by an incredibly sophisticated set of tools such as random matrix theory, which are exotic even for professional researchers. Perhaps it would be better to spend more time explaining the concept of stochastic volatility or nonstationarity than rocketing the reader into unknown grounds...

I come to the conclusion that the aim of the book is more to impress the reader about the technical sophistication of the authors than to teach anything in a clear manner.

Although OK as a bedtime reader, this book certainly does not contain anything one can practically implement: in fact the presentation is so imprecise that one is lost in the successive and uncontroled approximations, not knowing at the end what is the algorithm proposed to solve a given problem.