Quants mine gold for new market-making model

Banks that make markets in gold typically hedge the spot price with futures. Standard models assume the two instruments are highly correlated, and because the bid-ask for futures is often tighter than the spot spread, it makes sense for dealers to hedge with futures.

But standard pricing models might not have the full picture. A new paper published in sister title Risk.net this month suggests the connection between spot and futures prices in gold markets might be stronger than standard correlation.

“They are cointegrated,” says Olivier Guéant, professor of applied mathematics at Paris 1 Panthéon-Sorbonne University, of the relationship between the spot and futures markets for gold, “which means the difference between the two is stable over time. It’s not diffusive, but rather it oscillates and it’s statistically stationary”.

This also means the difference – known as the exchange-for-physical (EFP) spread and often simply referred to as ‘the basis’ in the industry – is mean-reverting.

The authors believe the extra steps taken to determine the actual point of mean reversion leads to a more accurate representation of real markets

That observation opens the door to a new approach to making markets in gold – and potentially other precious metals and even currencies.

In the model proposed by Guéant and his co-authors – Alexander Barzykin, director of global FX and commodities at HSBC, and Philippe Bergault, associate professor in applied mathematics at Paris Dauphine-PSL University – spot gold is simulated by an arithmetic Brownian motion. The novelty is in the modelling of EFP as a random process – specifically, a nested Ornstein-Uhlenbeck process – that reproduces not only the mean reversion but also simultaneously makes the reverting point itself a mean-reverting process.

“We then need to estimate the parameters of these variables, and we use stochastic filtering to estimate the actual point of mean reversion,” explains Guéant. “On top of this setting, we apply stochastic optimal control, as the objective is to maximise the risk-adjusted P&L of the market-maker.”

The modelling of the EFP is complex, but the authors believe the extra steps taken to determine the actual point of mean reversion leads to a more accurate representation of real markets.

The project was born out of the real-world experience of HSBC’s precious metals desk, which led Barzykin to conclude that EFP should be modelled with two layers of mean reversion.

The problem with a simple mean-reversion is that market-makers that build a position that relies on the EFP spread closing swiftly could incur sizable losses if the convergence fails to happen, which the data suggests is a common occurrence.

“You can lose quite significantly if you rely on just intraday mean reversion and don’t include a layer of protection, because, albeit cointegrated, EFP fluctuates a lot with dynamics on multiple timescales,” says Barzykin.

The final model outputs the best action for traders to take in any given scenario, from adjusting bid-ask quotes to trading on the futures and spot price. It allows market-makers to quote tighter bid-ask spreads to clients by trading futures more efficiently than standard models that assume the two instruments are simply correlated.

“The advantages I see in this framework is that it helps us efficiently manage risk with access to cointegrated liquidity,” says Barzykin. “As a result, we are able to provide better pricing to clients, particularly for larger trade sizes.”

While the paper focuses on making markets in gold, the authors say the model has wider applications. It can be equally applied to silver and any other metal for which there is a spot market and a liquid futures market. The researchers are also testing its use in currencies and think that, with adequate adjustments, it could even be applied to corporate bonds.

“There are other examples in FX markets where this model will be applicable, particularly in Asian currency markets, such as Indian rupee non-deliverable forward (NDF) against Indian rupee onshore,” says Barzykin. That is because NDF and onshore markets for the rupee are also cointegrated.

Perhaps the most intriguing application is for corporate bonds, which display cointegration across different maturities and seniorities. But that would require an extension of the model to a multi-dimensional framework to deal with more than two variables. That is a project the researchers are planning to work on in the future.

Guéant also has other, more ambitious ideas. “Another avenue of research would be to be able to add more adverse selection elements into models,” he says. “That would be the holy grail of market-making modelling.”