Mathematics and Finance Hand in Hand

4 minute read


This week's blogging cause is an effort of putting together my recent random thoughts on the relationship between maths and the financial market. In the recent two decades or so, there has been a coup d’etat in the financial trading world, where human decisions have been largely replaced by sophisticated computer systems.

On a nothing but normal day of April in 2013, a fake news on Twitter saying "Breaking: Two Explosions in the White House and Barack Obama is injured." gathered a large amount of attention. An overresponse from Wall Street can be seen by a huge jump of 140 points within seconds in Dow Jones Index. Minutes later, the market quickly recovered to normal as this turned out to be a hoax.

In a hindsight, the fact that a small fake tweet can trigger such high waves is a bit worrying. Clearly, the hustle happened in seconds was not directed by real-time human decision making. Why? A) The flow of information can not be done in seconds among a number of traders; B) We humans are able to, although not easily,  use our rational mind to distinguish whether something like this is fake news or not; C) Are you sure checking Twitter during working hours is allowed for those traders whose eyes are fixed on the trading screens all day?

Of course you don't even need to use your toe to figure out that this almost instantaneous response of the market was triggered by those fine-tuned super computers. Indeed, such quick response should be accredited to some sophisticated modelling schemes that catch sensitive words in social media to make online predictions about the market performance. So what's actually happening behind the scene is, the selected few genius human minds created smart algorithms trying to mimic the market dynamics and automate the human decision making process. This is what's happening in the financial sector in recent years with the development of computer power and the boon of big data.

Let's ignore for a moment the fact that a completely computer automated trading decision without the interference of human judgement could possibly be very wrong, we do need for sure the interference of mathematics coupled with computational power to enable analysis of historical financial data. People in the financial sector mostly belong to one of the four functional components: sales, structuring, trading, derivatives research (aka "quants"). Most people would agree that quants' job contains the most intriguing part - maths. "Quants" are traders who use all kinds of mathematical modelling schemes to make financial trades. Indeed, they are the mathematicians in a room full of computers filled with reams of data. One of the most frequently used mathematical tools by quants is called the Black-Scholes equation.

The equation, first worked out in 1973, has led to wild applications in the options market, and thus an explosive number of trades made based on it. Although it provides accurate assessment of the value of options, it has its Achilles' heel. It assumes the movements in share prices resemble the movement of particles in liquid. However, this more often than not, disagrees with the reality. The financial world is much more filled with fat-tailed distributed data than in the physics world. The 2008 financial crisis, is no doubt an evidence of the failure of the Black-Scholes equation in some extent.

Obviously, the urgent need to tame risk in the financial sector cannot be settled without a good understanding of the mathematical model being used, and the realisation of the model's drawbacks. Also, any automated modelling schemes alone would not suffice to yield successful decision making (or money making if you like) without sensible human judgement to take in.

Have those big and small financial crisis through out the years cast any light on financial modelling? Well, first we need to think through the relationship between mathematics and finance. Finance people, do never fully rely on mathematical modelling. They are never a perfect simulation of reality. Those financial moguls, who fought in 2008 found themselves racking up daily losses that the computers said should occur only once in millions of years, learnt this lesson the hard way.

Finally, let me end with this blog with the thought-provoking TED interview of Jim Simons, possibly the richest mathematician and the smartest brain in hedge fund. Mathematicians surely have done dandy in hedge fund industry. Definitely, a financial world with more mathematical savvy people would be a better world!