Alain Ruttiens on his book, The Mathematics of the Financial Markets

In this interview I talk with Alain Ruttiens about his 2014 book: The Mathematics of the Financial Markets: Financial Instruments and Derivatives Modeling, Valuation and Risk Issues.

Published: 10 January 2014

In this interview we talk with Wiley Author, Alain Ruttiens about his new book: Mathematics of the Financial Markets, Financial Instruments and Derivatives Modeling, Valuation and Risk Issues.

Alain is an Affiliate Professor at ESCP Europe Paris campus, where he teaches Mathematics of the Financial Markets. He holds a Masters Degree in Chemical Engineering (Faculté Polytechnique de Mons, Belgium), with a further degree in Operational Research (FUCAM, Mons, Belgium). Most of his career has been in the banking sector (Banque Indosuez, then KBC Bank), mainly in the trading, research and development related to financial derivative instruments.He is founder and asset manager of a hedge fund, and works as a Partner of NEURON sarl, where he is active in consulting on financial markets, in Luxembourg.

Jacob Bettany: Could you begin by telling us a little bit about your background and what motivated you to write this book?

Alain Ruttiens: My background actually played a significant role in this book. First, my education, MA in Engineering: I have a pragmatic approach to maths, that is, an applied mathematics orientation. Second, I did not start my career in the financial markets world, so I had a lot to learn about becoming able to trade then to set up trading of new instruments as I did for many years, mainly with Banque Indosuez. Third, I have a lot of teaching experience, first internally in Banque Indosuez, then later on as an affiliated professor at ESCP (one of the leading business schools in France) where I am still teaching “Mathematics of the Financial Markets” in their master of finance program, but I also teach in some other places, including in executive masters and in executive training programs, thus facing people who are professionally concerned by financial markets. I have written other books and articles about financial markets and instruments, but I needed a book to support my courses, and so this book is finally the sum of my teaching and market practitioner experiences, centered on quantitative finance applied to the financial markets.

JB: How is your book structured, and why did you make those choices?
AR: My objective was twofold: first, to set up the quantitative, mathematical material covering the widest possible range of financial instruments, from the most basic ones – such as forex instruments or bonds – to the most “advanced”, such as credit derivatives, volatility and correlation. Second, writing the text with the greatest care for pedagogy. Like many others, I presume, I have been so many times confronted with unclear writing, overlong developments and lack of adequate examples. I wanted to systematically illustrate the theoretical developments by examples, always based on real market data. For example, when explaining the (G)ARCH  family of processes, I give an example of application of the main ones, which is far from common in other books…  Also, for similar pragmatic reasons, I adopted the following principle, regarding the question of formulae demonstrating: if some formula proof is useful – brings some “added value” in the understanding of the topic treated – , I give it in the book, e.g. the Black-Scholes formula, or how to price a forward, or a swap. If not, I do not give it, but when the proof is not easy, I give the reference where to find it, as for example, about the Heath-Jarrow-Morton model for interest rates. And in some cases, if a resulting formula looks surprising at a first glance, I give the proof in an Annex to the related chapter, not to take up too much place in the course of the text, this is for example the case of the proof of the Itô lemma.

JB: There are a lot of books out there which cover these topics, what makes yours stand out? Why should people buy this book?
AR: Actually, as of today, there is only one book having a rather similar scope, which was published after I sent my manuscript to Wiley. As a matter of fact, there are several books which, either, mix some mathematical, quantitative content of mine, combined with chapters dedicated to the use of the financial instruments, or books more centered on mathematical developments without considering their applications to financial instruments, such as books on the stochastic calculus, or, on the contrary, only presenting a very basic mathematical content, or else, restricting their content to a part of my scope, such as, books about options, books covering a wide range of spot and derivatives in the forex market, etc. In this last case, such more specialized books may go further into mathematical details and coverage. By contrast, my aim was to deliver a “first entry” book, although sophisticated, covering all the financial instruments, and restricted to the mathematical stuff, presented in the most comprehensive way.

…just because it is a book about financial maths doesn’t mean that it must look like a PhD thesis!​

JB: Who is the book aimed at, and what level of expertise is required to understand the book?
AR: The book is aimed at two main groups of readers. First, market practitioners who need to master the quantitative underlying of the financial instruments they handle, such as traders, risk managers, or any other related activities (sales, IT, etc.); second, to students in finance, more specifically, in the subset of financial markets.

As regards the level of the reader’s expertise, first he’d better have some practical knowledge of financial instruments. Second, regarding the mathematical level needed to understand the book, it is limited to basics, after all: the reader should know basic things such as the meaning of log and exponential functions, differential equations, and a (very) minimum of integral calculus, plus the basics in probabilities and statistics (the Gaussian distribution, mean, standard deviation, variance, and some understanding about the kurtosis and the skewness of a probability distribution). Also, by comparison to several (although good) books, mine is easier to enter into, for a non-mathematician, because it does not introduce key concepts in a purely academic way, that consists in aligning theorems #1, 2, 3, etc, interspersed by numbered lemma and propositions, each one followed by lengthy proofs that are sometimes difficult to digest and which do not necessarily bring a clear understanding of the subject: after all, just because it is a book about financial maths doesn’t mean that it must look like a PhD thesis! And at least, I always take care to translate mathematical formulae into plain English…

JB: What would you say are the most difficult topics you cover, and what were the challenges for you personally in writing this book?
AR: One of my main challenges was to keep an equilibrium between what had to be covered in the book, and what didn’t (but in this last case, inviting the interested reader to go further through the bibliography that ends each of my chapters). Actually, I always tried to determine what is actually crucial for a market practitioner to know about the quantitative underlying of what he is playing with, and what is less important. To achieve this, I was of course helped by the fact that I wear two hats, that is, market practitioner and academic. Also, I wanted a well summarized text to keep the length down. I was often faced with the difficulty of extracting clear views from long developments. As regards my “most difficult topics”, they mainly relate to the most recent and most complex mathematical valuation models, such as for example interest rates modeling, volatility modeling, and credit derivative modeling. But even in these chapters, I tried hard, on top of the mathematics, to offer a clear presentation of such complex topics.

JB: How your view, has the emphasis in Mathematical Finance changed since the financial crisis of 2007? And to what extent do you address issues raised by the financial crisis?
AR: This crisis showed extraordinary consequences, with respect to mathematical finance. First, it revealed to many people, although concerned by the management of financial institutions, the pervasive importance of instruments valuation. For example, the subprime crisis highlighted the importance of both correlation effects and of credit risk quantitative measurement. As of correlation, it is a fact that, up to now, no correlation model exists. This implies that not only securitization tranches but also basket derivatives are potentially dangerous. And with respect to credit derivatives, there exist many models, but none are satisfactory. Indeed, as I cover it in the conclusion of my chapter about credit derivatives, and more generally in my last section (Chapter 15.2 Potential troubles with derivative valuation), one of the key problems is the absence of a theoretical, fair pricing model that is exogenous: for most of financial instruments, such exogenous models are common. For example, you determine the fair price of a forward contract by combining a spot price and two spot interest rates, i.e., an exogenous information, not involving observed market (forward) prices. But if, for credit derivative, you use an endogenous information, i.e. observed credit derivative market prices, or, more generally, if for some models you have no other choice than “calibrating” it on existing market prices, the danger is obvious. During many years before the 2007 crisis, I drew attention to this problem in my courses and executive training sessions, and added that this could lead to market troubles, of course without acting as a guru… having no idea about when a crisis could occur, nor of its size. Another observation I have made, is that if, on the one hand, the financial community is now aware of the dangers, on the other hand, its behavior has not really changed. And it is not the tsunami of banks and funds regulations that will solve the problem, such regulations aiming mostly to ease the regulators’ and controlled institutions’ conscience. The best proof is that financial institutions continue to incur from time to time huge financial losses, even if these losses do not necessarily reach the critical peak of what we faced in 2007.

…the very first engineers were those Romans who built road structures to allow the traffic of Roman troops all over Europe: when they had finished a bridge, they were forced to stay under the bridge while soldiers were crossing the bridge: if it was not strong enough, the engineer was the first to die, but if it was ok, he did not receive any bonus. Just the contrary of the traders…​

JB: You have discussed how things have changed historically, would you care to speculate about how things will change in the future?
AR: I am afraid financial crises are not helping to significantly change financial market activities. If changes will occur, this will be more under the form of pursuing the current trend of regulations, with more and more costly constraints which do not necessarily – far from it – reach their goal of reducing the risk of collapses of stakeholders in the market. Alternatively, this could lead to a reduction in the market’s activity as a whole, which is not necessarily a good thing. The real economy needs financial markets, both spot and forward (including conditional forward products such as options), not only for hedging purposes, but also for well understood and well mastered speculative operations. After all, generating revenues for pension schemes, and saving in general, implies speculative operations, but conducted in a safer way. If I do not expect real changes in markets and institutions behaviors, it is because of the excess of greed of financial institutions managers (and shareholders), who favor a quick and substantial return, simply because of their own revenues under the form of bonuses and equivalent schemes. The issue of reconsidering such bonuses and equivalents is not (yet) really questioned, or has been handled in the wrong way (through public authorities), and so traders and their management will continue to benefit from their positive performance, but will not be financially punished for negative performances, except in extreme cases. An example I use to emphasise the importance of this is the engineer’s mind: through their education, they have in their genes the ancestral behavior of the very first engineers, who were the people building cathedrals in the Middle Ages, for example: they were aware of their lack of knowledge about strength of materials, and so they deliberately built pillars which were too big, that is, with enough safety margin to avoid their buildings collapsing, yet there were no norms (regulations) at that time! And indeed, these cathedrals are still standing centuries later; I dream that traders and their management would accept a reduction of leverage and profit margin requirements for the same reason… And moreover, never forget that the very first engineers were those Romans who built road structures to allow the traffic of Roman troops all over Europe: when they had finished a bridge, they were forced to stay under the bridge while soldiers were crossing the bridge: if it was not strong enough, the engineer was the first to die, but if it was ok, he did not receive any bonus. Just the contrary of the traders…

JB: What are your views on the way that financial mathematics is taught in universities?
AR: I notice that, mainly, it is quite well taught. Of course, there are professors who benefit from financial market experience gained through expert or consulting activities aside of their academic task, making their course more attractive for the audience. However, I regret two things. First, not all business schools are splitting their finance content into corporate finance and financial markets subsets in the same way. If the balance is too much in favor of corporate finance, the students run the risk of being insufficiently prepared to face financial markets issues, even within the framework of a corporate career. Second, regarding the content of courses dedicated to financial markets, and in particular with respect to their mathematical features, I notice that there are some important topics which are more or less badly served (the same applies to books as well!).

…The book is aimed at two main groups of readers. First, market practitioners who need to master the quantitative underlying of the financial instruments they handle, such as traders, risk managers, or any other related activities (sales, IT, etc.); second, to students in finance, more specifically, in the subset of financial markets.​..

As an example, this is typically the case for swap valuation, despite today the swaps market being the second biggest financial market (number one being the forex spot market)!: there are not enough informed teachers who are able to distinguish what needs to be developed and what is irrelevant, so that I know of courses that not only develop useless notions, but also miss those which are absolutely critical for mastering the product, or come with impractical calculation methods. I also feel that some courses are not focusing enough on the risks associated with existing pricing models, mainly due to their related hypotheses. And, in mathematics of the financial markets courses, do you often meet, associated to a price determination, the importance of its related confidence interval? Again, this confidence interval feature is mainly due to modeling hypotheses, and this may have heavy consequences on risk management!

JB: There is a view that hardware advances in parallelisation require new mathematical approaches and a renewed focus on matrices and their transformations. Do you have an opinion on this?
AR: Unfortunately, I have no experience in hardware and software computational issues. Your point is calling to my mind, because I had in mind that matrices and matrix transformations were a very classic, well mastered area of the maths! Besides, in my personal point of view, there are other issues that dramatically lack of suitable mathematic solutions, such as correlation modeling as already mentioned. But also, I am concerned about two key issues. First, a crucial feature of the financial markets behavior, that is – on the contrary to physics and natural science – the un-fixed nature of the phenomena we study, since financial markets is a human science. And second, the difficulty to statistically handle (very) low probabilities in a satisfactory way. This last problem is affecting a lot of situations in products valuation involving the well-known “fat tails” problem, but also involving the core of credit derivatives valuation, a default being, fortunately, a rare event. In particular, research in the field of copulae appears very problematic; remember the dramatic consequences of using the Levy’s copula… I personally have no idea of the right solution, but I feel one should try to use other ways, at least because copulae are based on too restrictive hypotheses.

JB: Thank you very much, Alain.