Almost 12 years that I’ve found out this article in Le Soir [Full article, in French: https://www.lesoir.be/art/maudite-mathematique_t-20081114-00K1HJ.html]. I remember the scene: back in the train from my job as Front Office Quant, working precisely on CDO modeling in the trading room of a major European bank. One year after the CDO crisis started, the mainstream speech was to blame Quantitative Analysts and, more generally, the extensive use of maths in finance. “Finance is a field of management/social science. How could people be stupid enough to rely on complex maths to achieve this ?”
And this was the coming out of Li’s Gaussian Copula (standard market model to quote CDO prices; see picture) to the broad audience. And the tone was close to this : “Look at this impossible-to-understand formula, full of letters here and there ! How could people really understand that ? How come that you need a PhD in physics to get the meaning of this ?”. At the same time, people busy solving the issues with the hands on were thinking instead “How naive are they ! How could they think that such a simple formula, merely containing a couple of constants, could be complex enough to adequately model the risks underpinning CDOs ?” . Li’s formula is at the level of Master 1 in Business Engineering. There is nothing difficult behind. It is a “toy model” that has value to understand the general impact of some basic sources of risks. Yet, it is arguably a huge simplification of reality. The problem in the crisis did not come from “too advanced maths”. The problem came from the fact that financial products became increasingly complex, and that to adequately assess the underlying risks, you cannot make the economy of a sound modeling approach. The development of this business line was so fast that the models behind couldn’t follow. The problem was that, given the products, the models were not realistic (i.e., Evolved) enough.
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Like it or not, we are living in a complex world. Technology is everywhere and, behind technology, there are mathematical models. For instance, designing and selling probabilistic models has actually become the primary business of Amazon. It is weird to agree that the world changed for everyone but, at the same time, asking banks to keep on doing the same business as they did a couple of centuries ago. Investors and companies face difficult problems related to increasingly complex risks; they need advanced financial services, and someone needs to help them mitigate those risks. Clearly, neither intuition nor ABC maths can be enough for this purpose. What we do need is, instead, skilled managers, able to assess and understand the complex reality underlying their business.
We cannot send complexity behind the carpet. We have to face it, and give ourselves the means to tackle it.
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PS: the formula in the picture gives the probability that loan i defaults prior to t conditional on a Normal systemic factor M representing the state of the economy. N stands for the standard Normal CDF, rho is the Base correlation (accounting for the dependency accross defaults) and Qi(t) is the probability that borrower i defaults prior to t..
Source: https://tholansonnha.com
Category: Finance
