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.