# The Commonest Mistakes in Quantitative Finance: A Dozen Basic Lessons in Commonsense for Quants and Risk Managers and the Traders Who Rely on Them

## Introduction

Judging by research papers and books on quantitative finance, and from conversations with thousands of practitioners, not to mention well-publicized modelling mistakes, I believe that quants have totally lost the plot. They focus on making models increasingly complex when they should be making them more robust. They use the most abstract of mathematics and then make obscenely simplifying assumptions. They fine tune irrelevant detail and ignore fundamental issues of risk management. They obfuscate when they ought to educate.

Much of quantitative finance is dumbed down for the masses, partly, I am sure, to sell lots of books on the subject - there are sadly more non-mathematicians in the world than there are mathematicians. This is not too dangerous because you can't do much quant finance without mathematics, and therefore you can t really invent too many toxic contracts. But there are also at least as many people making quantitative finance too complicated. Overly abstract mathematics is being used by people who have never traded, yet whose models are respected precisely because of their complexity. These models (and people) are dangerous. Lack of transparency in financial models is not good. Given that the models can never be perfect in this 'soft science, why is there so much focus on detail at the expense of the big picture? Some are easily blinded by science, unable to see the wood for the trees.

For the above reasons, and after many years experience in research, training and practice, I have come to believe in a mathematics sweet spot, using the right kind of mathematics for each job, not dumbing down and not making too sophisticated; a level of mathematics such that people can see what the assumptions are and where lie the weaknesses. Ideally spend more time seeking robustness of a model rather than trying to make it 'better.' Sadly, 'better' these days seems to mean simply adding more and more factors. It is easy to impress people with difficult mathematics, but a quant's job is not to impress, it is to allow banks and funds to trade products, perhaps new products, and to trade profitably and with well-understood and controlled risk.

In this chapter I outline 12 of the most common causes of errors in quant finance. These 12 lessons are most definitely not about inverting your transform, or about convergence of Monte Carlo simulations, or how to speed up your calibration of Hull & White. Those are precisely the sort of questions that should only be asked after the more fundamental issues have been successfully addressed. This chapter is about the fundamental issues.

All of these lessons are basic, all of them are easily quantified, all of them have cost banks and funds huge sums of money, and all of them are still under-appreciated. In 2000 I wrote, 'It is clear that a major rethink is desperately required if the world is to avoid a mathematician-led market meltdown' (Wilmott, 2000). In 2006 I wrote about credit 'some of these instruments and models being used for these instruments fill me with some nervousness and concern for the future of the global financial markets. Not to mention mankind, as well. Never mind, it's probably just me' (Wilmott, 2006a). The first draft of the chapter you are reading was written in mid 2007. I am putting the finishing touches to it in late 2008 when it has become apparent that the man in the street has also been dramatically affected by our 'high finance.'

If you think quantitative finance is only about the likes of Radon-Nikodym derivatives, squared Bessel processes and numerical quadrature in the complex plane, then this chapter is not for you. If you think quantitative finance is more interesting than that, read on!

The subjects are:

• Lack of diversification

• Supply and demand

• Jensen's Inequality arbitrage

• Sensitivity to parameters

• Correlation

• Reliance on continuous hedging (arguments)

• Feedback

• Reliance on closed-form solutions

• Valuation is not linear

• Calibration

• Too much precision

• Too much complexity

But first a simple test-yourself quiz, to encourage reader participation!