The Volatility Surface: a Practitioner’s Guide does not come across as a practitioner’s guide. There are gems of practical wisdom, but these are hidden deep within pages of arcane mathematics which, in my opinion, should be in the appendix if they are to be included at all.

This criticism is not primarily centred on the difficulty of the mathematics: volatility is a difficult subject so I wouldn’t expect any proper treatment to be straightforward. Rather, the book is too mathematical in the sense that even when I bit the bullet and worked through some of the derivations in full (dusting off some of the Mathematical Methods lecture notes from university), they seldom gave much insight. Rather than being a “practitioner’s guide”, the book comes across as a follow-along exercise book for students taking his lecture course at NYU to pick up some mathematical tricks.

Furthermore, the organisation of the book is bizarre. Jargon is introduced without explanation; subjects are discussed without being put into context; figures and tables are inserted with little reference or commentary. One gets the impression that this book was a rather hasty compilation of lecture notes into textbook format.

All this said, there were parts of the book that I liked: the treatment of jumps and default risk were pitched at the right level of detail, with a clear emphasis on practicality. Gatheral also does make valuable points regarding the qualitative differences between stochastic volatility fits and local volatility fits, though you have to dig through the book to find these.

Perhaps my criticisms are unfair. I presume the target audience for this book is a sell-side derivatives quant, which I certainly am not. Nevertheless, I got a lot more out of Maxime de Bellefroid’s The Derivatives Academy, which contains many of the same insights in a much more accessible format, though it sometimes lacks detail (and in many cases references Gatheral!).