The machines are coming for your pricing models

Deep learning is opening up new frontiers in financial engineering and risk management

Financial models are not perfect. The markets are so complex that to explain their behaviour, models make all sorts of simplifying assumptions, leave out lots of the details and try to capture the main dynamics.

The Black-Scholes options pricing model, for instance, ignores trading costs and assumes that stock prices follow a random path, with constant volatility and drift.

Everyone knows these assumptions are not really true. Good traders treat financial models as a guide and use their experience and intuition to fill in the gaps. Failure to do so is often costly.

Getting a computer to exercise that kind of human judgement is difficult, as a team of quants at JP Morgan discovered when they tried to automate the hedging of one of the firm’s derivatives portfolios. Automated systems that rely on classical models such as Black-Scholes are destined to fail when markets defy model assumptions, which they do all the time.

Click here to read’s in-depth feature on deep hedging and the end of the Black-Scholes era

So the JP Morgan quants tried something different. Instead of feeding the machine a model, they let it formulate its own hedging strategy. An artificial neural network was trained to identify patterns and relationships from historical data. It then used a technique called reinforcement learning to refine its strategies based on simulated trades.

The result of the experiment will come as no surprise to anyone that has been following recent advances in artificial intelligence. The so-called ‘deep hedging’ strategies developed by the machine outperformed existing ones based on classical models.

Last year, JP Morgan began using the self-taught algorithms to hedge some of its vanilla index options portfolios. The bank now plans to roll out similar technology for hedging single stocks, baskets and light exotics.

Deep hedging feels like the start of something big in quantitative finance. Several other firms, including Bank of America and Societe Generale, are working on similar projects. Some quants are already talking about a future of “model-free pricing”.

But the machines are not infallible. Their performance is heavily reliant on the data used to train them, and errors in the training data, no matter how small, can make the resulting strategies very unstable. And even a well-trained machine cannot generalise or extrapolate beyond its training data, so it must be retrained every time there is a structural change in the markets.

Deep hedging feels like the start of something big in quantitative finance

The other problem is interpretability. Machines are not very transparent. Neural networks have complex structures and comb through millions of data points, which makes it hard to pinpoint how they come up with answers, or why something went wrong.

To operate these machines safely, humans will have to learn new skills. “People who today spend their time adjusting for the deficiencies in classic Greek-type models now need to understand how the statistics work,” Hans Buehler, global head of equities analytics, automation and optimisation at JP Morgan, said in a recent podcast.

JP Morgan is taking steps to address this. Last year, it hired Manuela Veloso, head of the machine learning department at Carnegie Mellon, to lead its artificial intelligence research efforts. Part of her job involves explaining the workings of the bank’s various machine learning projects to supervisors. The bank is also training its staff to use Python programming and has made Jupyter Notebooks – a web application that is used to create and share data analysis – available to trading desks.

Unless humans learn to properly use their new machines, this generation of models will fare no better than the previous one.

Only users who have a paid subscription or are part of a corporate subscription are able to print or copy content.

To access these options, along with all other subscription benefits, please contact or view our subscription options here:

You are currently unable to copy this content. Please contact to find out more.

You need to sign in to use this feature. If you don’t have a account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an individual account here