Mathematical Modelling in Finance, Sports, ....

This article first appeared in the December 2008 issue of it magazine. This is part of the Folk Technology series that I write every month.

Would the current financial crisis have occurred if objective, number-crunching machines had been taking decisions rather than human beings driven by intuition and instinct? Perhaps, it's time we took a closer look at the potential of mathematical modelling.

It may sound like something out of a school textbook, but mathematical modelling is taking the world by storm, albeit without too much fuss.

In basketball, baseball and many popular sports, suggested player salaries are arrived at using mathematical modelling.

Banks in India and abroad often use mathematical risk modelling to determine whether or not to give you the home loan you are seeking. Even Google uses mathematical models to determine auction bids on keywords. The examples don't end there -- today mathematical models are used in diverse areas.

The rise of mathematical modelling

Mathematicians have had tools in their arsenal to perform predictive modelling since the nineteenth century. But the recent adoption of mathematical modelling in the other diverse areas is the result of society's familiarity with computers and an acceptance of the fact that computers are indeed better at crunching large numbers than humans. Today people are willing to let computer programs manage their funds, but would they have been open to the idea 10 years ago, even though a computer, Deep Blue, had beaten the reigning chess champion, Gary Kasparov?

So how do these models work? In chess, given the current board position, the computer tries to make a move that will give it an advantage over the opponent. This means the computer program has to calculate all possible board positions and select the best move based on a prediction of the outcome of the game, given that move.

To predict a stock's price or a player's salary, the mathematical models used can be explained as predicting future trends based on the past scores. So a player who has consistently scored runs in the recent past would get a better price. Older scores would be damped by an appropriate scaling factor so that recent playing ability is given more weight in determining the salary. Criteria like popularity can also be factored in, based on measurements of number of mentions in blogs, news articles, etc.



Similarly, banks decide on your home loan application by predicting your repaying capacity based on current and past salaries, employment history, educational qualifications, credit history, etc. In addition to your own potential, they also model the future health of real estate markets. The model can include as many parameters as necessary and can keep evolving over time.

Why models succeed

In the 20-match world chess championship held in 1995, Vishwanathan Anand scored the first full point in the ninth match, but went on to lose against Kasparov because of the latter's intimidating tactics. Kasparov declared after the match that Anand was good at chess but was not psychologically up to the task of playing him. Interestingly, folklore has it that Kasparov lost to Deep Blue in 1997 because he couldn't stare it down. Today, it is debatable whether a computer program can beat Anand. But chess computer programs can, without doubt, play almost as well as a chess grandmaster (there are only about a 1000 grandmasters today). Deep Blue could evaluate 200,000,000 chess positions in a second. In the recently concluded world chess championship, Kramnik got into time trouble in the matches he lost against Anand precisely because he was trying to optimise his next move by trying to calculate all possibilities in his head. Deep Blue definitely wouldn't have had any such trouble.

Most chess players have an excellent memory. A player like Anand remembers thousands of chess moves. But even Anand cannot remember more moves than a computer. So though a computer may be far less intelligent than even a five-year-old child, given its number crunching abilities and enormous memory, it can give a good fight and often win against an accomplished chess grandmaster. Remember, Deep Blue didn't have much chess knowledge. It was built by a team of five computer science researchers and one international chess master, who otherwise would have been no match for Kasparov.

A program that tracks stock prices can often do much better than a human being, as it can track huge amounts of data. For example, a computer program tracking shipping stocks can keep track of quarterly reports, weather conditions and pirate movements from news articles, offshore oil drilling trends, and a host of other factors that even a large group of human analysts cannot. In stock markets, speed is crucial. Based on the evaluation of a given set of parameters, a computer program can make split second decisions that may take hours or days for human analysts.

A major weakness of computer programs is that they do not have intuition or feeling. But this is also their strength. Would the financial crisis enveloping the US have come about if computer programs had decided whom to give housing loans to? Would derivative pricing based on mathematical modelling have warned us of the impending sub prime crisis?

The current economic slump has shown the need for better mathematical modelling of the financial markets. Even the last IPL biddings were driven to a large extent by sentiment. For example, Andrew Symonds earned a premium for the bad press he had generated during the preceding India tour of Australia. In hindsight, it turns out the franchisees overpaid for a lot of the players they bought. They would have been better off doing the bidding on a more objective, mathematical basis.

There is a distinct need for practical and usable mathematical predictive models in various fields. From sports to banking, such models can aid in better decision-making and importantly, there is realisation of this fact. As the Big Blue team showed, such models can be developed by small teams comprising people who are good at mathematics, programming and have an understanding of the domain for which the model is being built. As most science and engineering graduates will probably tell us, coming up with such models is not rocket science. With Chandrayaan successfully placed in the moon's orbit, perhaps they can now get down to solving this problem.

(Part of the monthly Folk Technology Series that I write for i.t. magazine)