“How about the scandalous stories of thousands of families with small and medium investments who have been ruined because of the greed of financial institutions in the United States and Europe. Look at the evictions, ruined families, and suicide attempts caused by the financial crisis of those who have failed to control the capital markets or the prices of raw materials. ¡Vaya mierda!”¹

—Response to the survey question: “Do you have any outrageous or hilarious stories that you think ought to be in Paul and David's new book? Share some details, please!” at wilmott.com

“The truth about their motivation in writing.”

—Response to the survey question: “What topics should definitely feature in the book?” at wilmott.com

The global financial crisis that peaked in late 2008, and whose aftershocks have yet to fully dissipate, was the culmination of many years of dubious financial practices. If carried out alone they might have caused only localized harm, but they became aligned in the way that only the most dramatic of astrologers can dream of: a quadrillion dollars in complex financial products that no one understands; risk-management techniques that hide risk rather than decrease it; moral hazard and dangerous incentives; lack of diversification; regulators that are oblivious; mathematicians acting as psychological enablers. It was a story where the naïve, the negligent, and the downright nasty all pulled together in seizing as much as possible for themselves while almost destroying the financial foundations of the planet.

Of course, things have moved on since then. The banking system has become even more concentrated. Global debt – the engine fuel of finance – has grown to unprecedented levels. Markets, in which activity is increasingly dominated by high-frequency-trading robots, experience constant “flash” events where prices suddenly go wild before returning to more normal levels. The world financial system is once again rattling at its cage, ready to blow. And quantitative finance – the use of mathematical models to assist or dictate investment decisions – has become more powerful and influential than ever.

The story, in other words, isn't over – not by a long shot. Indeed, the stakes have never been higher, which is why previously arcane topics such as hedge funds, high-frequency trading, and too-big-to-fail banks have become a major topic of often-confusing debate for everyone from TV pundits to politicians. And why the confusion is often deliberate.

It has been estimated that in 2010 the notional value of all the financial derivatives in existence was $1.2 quadrillion.² That's $1,200,000,000,000,000. For comparison, it's about 17 times the market capitalization of all the world's stock markets, or 150 times the value of the above-ground gold supply, or $170,000 for every living human on the planet. Actually, it's larger than the entire global economy. We'll explain this number, and how it could be interpreted, later. For the moment, let's just say that whatever it means in terms of risk, it seems like a dangerously big number for what is, let's be honest, just a service industry.

This book is not about the fallout from the crisis – plenty of books and column inches have been written about that – but about helping to prevent the next one (which won't look like the last one). To do that, it is necessary to go into the engine room of this massive shadow economy and understand how quantitative analysis works. How do you create a quadrillion dollars out of nothing, blow it away, and leave a hole so large that even years of the deliberately misnamed “quantitative easing” can't fill it – and then go back to doing the same thing, only faster? Part of a quant's job, as we'll see, is science, and another part (the one where mathematics is used to obfuscate reality) is the opposite of science. We will discuss both, starting with the science.

The book is divided into two main parts. The first five chapters dip into the history of quantitative finance and explain its key principles, such as risk analysis, bond pricing, portfolio insurance – all those gold-standard techniques, in short, which completely failed during the crisis, but have yet to be properly reinvented. We explore the elegant equations used in financial mathematics, and show how the deadly allure of their ice-cold beauty has misled generations of economists and investors. We trace the development of financial derivatives from bonds to credit default swaps, and show how mathematical formulas helped not just to price them, but also to greatly expand their use to the point where they dwarfed the real economy. And we show how risk-management and insurance schemes have led to more risk and less insurance than arguably at any time in history.

The second part is about the quantitative finance industry today, and how it is evolving. We will show what quants do, the techniques they use, and how they continue to put the financial system at peril. Part of the problem, we'll see, is that quants treat the economy as if it obeys mechanistic Newtonian laws, and – by nature and by training – have no feel for the chaos, irrationality, and violent disequilibrium to which markets often seem prone. The same can also be said of the regulators watching the system. We'll lower ourselves into the hidden caves of finance, with their “dark pools” navigated by swarms of high-frequency traders, and show how new ideas from areas such as complexity science and machine learning are providing analytic tools for visualizing and understanding the turbulent eddies of financial flows. Along the way, we will grapple with some of the philosophical and practical difficulties in modeling the financial system – and show how models are often used less for predicting the future than for telling a story about the present.

The authors are both Oxford-trained applied mathematicians, who have worked in a variety of industries but otherwise come to this project from different angles. Paul is a quintessential insider – named “arguably the most influential quant today” by Newsweek – but he is also (as visitors to quant forum wilmott.com will know) a longstanding critic of standard practices. David works primarily in the areas of mathematical forecasting and computational biology (he invented a program called “Virtual Tumour,” which gives you an idea). He has argued in a number of books that economics needs to take a similarly biological approach – and that our out-of-control financial sector is in serious need of a health check.

The Money Formula provides new insights into one of the largest, best-paid, but least-understood industries in the world – and the one with the most capacity to either help our future economic development or give it the financial equivalent of a cardiac arrest.

We begin by turning to the early 18th century, when France was seeking financial advice from a mathematician.