Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management

Outstanding book, well worth the time to study carefully. Appreciate the emphasis on real world models/statistics rather than idealized approaches so prevalent elsewhere.

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 is one of my favourite books in Quantitative Finance.I agree with Paul Wilmott's back cover comment that this book has a plethora of ideas. I have one on my desk and another at home, and I check them frequently for new ideas.The Econophysics flavour is defended with elegance. It can be summarised as an approach based on empirical data, where there are not a priori assumptions on the distributions. In fact, this approach is more "scientific" than some dogmatic, axiom-based approaches in Economics like Efficient Market Theory or normality of returns. Moreover, checking directly the moments of the distribution is to my eyes more sincere than assuming X o Y distribution and fit its parameters. Of course, Statistical Physics may have a bias towards Lévy (i.e. power-law) distributions for the tails, but the authors prove that it is quite common to see this in real returns.The most important thoughts in the book are:* Returs are not normal, rather power-law on the tails* Not only mean and variance are important: third and fourth moments (skewness and kurtosis) are crucial for risk management* Using Taylor expansions on the empirical distributions we can estimate the first four moments or cumulants* Returns exhibit auto-correlation at high frequencies (around seconds), which decays as a power law and eventually (after 30 mins) dissapears* Correlograms (i.e. lagged auto-correlation) can help to understand the market impact of trades* Random matrices can be used to assess cross-correlation in a very robust way* Pricing formulas like Black-Scholes can be corrected with skewness and kurtosis, e.g. the smile and the deltaThere is however a small negative point: its very difficult notation. I think the book tries to target people outside Statistical Physics, but unfortunately the notation has shunned some people away from the book. I know the notation (just as Einstein's) is compact and elegant once you get it, but if on the first two chapters there were a "translation" of formulas in terms of sum operators and quotients, that would help people to climb up the learning curve much faster.I understand the book is a reference manual for seasoned professionals in Quantitative Finance, not a textbook. However, some extra pages to allow more explanations and examples would be nice for the next edition. Those additions could help non-physicist readers to understand those "stylised facts" of markets, especially when the ideas are very intuitive and should help question the mainstream approach in Finance and Economics.I think the notation issue is important, but it can be overcome with patience. This in my opinion puts the rating of the book closer to 5 stars than to 4.

To read about finance and derivatives

The equations are too small in kindle, so small that you have to zoom in to see the subscriptions. I returned it right away.