Stephen Blyth

Oxford University Press, 175pp

If one were to write a creation myth for modern finance, the wave of mathematicians and physicists who left academia for Wall Street from the mid-1980s onwards would be at the heart of it. As Stephen Blyth recounts in the preface to his book, these quant pioneers knew virtually nothing about finance yet succeeded in building a vast OTC derivatives industry in the space of 25 years. Some of the foundations, such as the Black-Scholes option pricing formula were already there, but most of the intellectual superstructure had to be built at the trading desk.

Blyth’s own induction to finance came in 1993 after two physicist classmates from Harvard joined Goldman Sachs. A PhD statistician, Blyth joined HSBC in London, and on his first day was asked to compute a bivariate normal integral. He soon began trading, working at Morgan Stanley as dollar options market maker and Deutsche Bank as proprietary rates trader. Finally his career came full circle: He was hired by Harvard’s endowment in 2006 and now combines trading with teaching statistics in his old department.

This textbook came about as a result of Blyth’s teaching activity, and it’s worth asking the question why such a book is needed now. There are already dozens of quant textbooks out there, going back to 1988 when John Hull first published ‘Futures, Options and Other Derivatives’. This encyclopaedic text is now in its ninth edition and close to 900 pages long. That’s before you get to the hundreds of journals, conferences and working papers devoted to quantitative finance.

However, Blyth has been critical of this quant industry for some time, in particular the way that experts devised clever formulas that were then used mindlessly for pricing and risk managing derivatives. In credit, the most egregious example was the now-notorious Gaussian copula, but other examples abound. Instead, Blyth argues, traders should focus on the logical consistency of what they are attempting to do. For example, that means ensuring that a particular asset isn’t described by several probability distributions at the same time.

For years, Blyth’s critique served him as a modus operandi in prop trading, helping him sniff out opportunities in markets where other traders were using models in a mindless way. Then came the 2008 crisis, when the most fundamental assumptions of quantitative finance—including those that Blyth assumed to be sacrosanct—broke down. That led to a flurry of new research as traders struggled to update their old models to incorporate counterparty or collateral risk, as well as new regulations such as central clearing, and a crackdown on abuses such as market rigging.

The crisis made the old textbooks out of date, and gave Blyth’s quest for logical consistency increased validity. That philosophy is the driving spirit behind his book.

Aimed at mathematically-literate readers with no financial knowledge, Blyth aims to kindle an interest in derivatives as an intellectual puzzle in probability. The book is structured around the theoretical assumptions needed to price derivatives and right from the start he pushes readers to think about the consequences of the assumptions breaking down.

Take the concept of arbitrage. Starting with forward contracts, the idea of no-arbitrage is a key driver of derivative pricing. To work, it depends on the existence of traders or algorithms sitting in the market trying to pick off discrepancies. After Lehman Brothers, these arbitragers—whose existence depended on access to funding and leverage—disappeared, allowing the discrepancies to persist for months.

Closely linked to arbitrage is the concept of risk-neutral probabilities, essential for option pricing. Using an intuitive binomial model, Blyth derives the classic result that the return of a hedged option portfolio is the risk-free rate. That leads him to the idea of martingales, the mathematical equivalent of a ‘fair game’ whose expected value tomorrow is the same as today.

By showing that a derivative (appropriately discounted) is a martingale, Blyth teaches his readers a powerful and general tool for pricing derivatives. While none of this new, Blyth’s approach is refreshing, for instance his exercise where readers get to show how two traders can collude by taking opposing positions and splitting bonus payments.

Blyth then moves to a continuous time limit, allowing him to derive the Black-Scholes formula. He then goes on to discuss interest rate products, his own speciality. Here Blyth’s philosophy of logical consistency comes to the fore. Rather than focus on complex price formulas for Bermudan swaptions, he invites readers to rank trades under different scenarios, getting them to think about the assumptions.

Blyth’s short book is unlikely to replace the likes of Hull in the near term. He avoids credit derivatives and commodity products, and doesn’t address current hot issues such as counterparty, collateral and funding risk. However, in the post-crisis world his approach to old results is refreshing and ought to be a template for the future.