Quants aren’t just passionate about maths and problem solving, they are passionate about new technology, about research and about applying new knowledge to existing problems.
Some might argue that models and computational finance has reached a kind of peak, after all, there is not that much excitement to be had with a 5% increase in the speed of a Monte Carlo. But Wim Schoutens, Professor of Financial Engineering at the University of Leuven, told delegates at QuantMinds International that developments in machine learning meant that there was still plenty to get excited about.
Old problems, new solutions
Schoutens is a veteran at this conference, having first presented some 15 years ago at Global Derivatives (as QuantMinds was known then).
“Back then we were busy trying to model the derivatives markets and come up with new and advanced models. We all know the result of that work, the Levy models, the variance-gamma model, the scholastic volatility models, the Heston volatility model, subjects that took up an entire stream of talks at QuantMinds for years.
“Later, there was computational finance, and how it could produce, in a reasonable amount of time, exotic option prices and speed ups for Monte Carlo, FFT models, and partial differential equations.
But that was the past, stated Schoutens. “Now you see on the QuantMinds programme there is a tsunami of Machine Learning (ML) presentations.
“I’m basically doing all three – an old problem, a computational model, and machine learning.”
Schoutens took an old problem – exotic option pricing – and a model with a limited set of parameters. He priced exotic options under that model, and subjected it to ML. The result was a tremendous speed up in computation.
“It’s actually not difficult, it’s fairly simple,” he explained. It’s old problems and traditional ML techniques. What might be a little bit new to you is the Gauss Process Regression (GPR),” he conceded.
Schoutens went through the process in some detail, but summed it up as follows:
“Once I have my set of data I’m going to send it to the gym. GPR can train there and once it comes back I have a tool that prices within an instant of a second your favourite exotic option under your favourite model.”
An alternative approach
GPR, he explained, was an alternative approach to the classical regression problem.
Of course not all problems are linear, he added, so the GPR is nonparametric. “It’s not that there aren’t parameters, it’s that there are infinitely many parameters,” he explained.
“What we end up with is a non-parametric approach, in that it finds a distribution over the possible functions that are consistent with the observed data.
“As with all Bayesian methods, it begins with a prior distribution and updates this as data points are observed, producing the posterior distribution over functions.
“I will limit things within a domain and I’m going to say that my function is not too wiggly. The way we do this is to use a covariance matrix to ensure that values that are close together in the input space will produce output values that are close together,” explained Schoutens.
The end result is that pricing an American option with almost the same accuracy is now 50 times faster.
“What’s the point in saving a fraction of a second? If you do it once, nothing. But if you have to do it continuously over time on thousands of underlying options, then this starts to get important,” he concluded.
“Even vanilla pricing, call options and put options under the advanced models can be trained.
“One of the applications I think that it will find its way to is structured products.
“Once you have issued the structured product, you take the model on which you want to value it and then you train it. Once it is trained, you don’t need to rerun your sophisticated model with your Monte Carlo simulation every time. What you do is take your GP regression and you calculate the price of that structured product with it.
“That is basically the story I wanted to tell,” he stated. “We have the simple old techniques of Gauss Process Regression. The essential thing is you have to invert a matrix, but software engineers have managed that, and the speed ups you get in these traditional quant models, after putting your ML, is in order of magnitude – it’s ten or even 50 times faster.
Wim will return to QuantMinds International this year to discuss Machine Learning for quant problems and Conic finance: Exploring new solutions to old problems including new dimensions of hedging, portfolio theory and trading.