It’s no secret that forex market makers balance most of their risk internally by matching client trades. There are good reasons for it. By internalizing risk rather than hedging on external trading venues, traders can avoid crossing spreads and paying brokerage fees. Customers also benefit as internalization reduces the impact on the market. But when volatility rises and customer flows become one-sided, market makers must quickly switch to external trading venues to hedge their risks. Whether to skew prices and wait for customer flow to even out, or hedge with other traders in the open market is a decision usually left to traders. But traders have little more than their judgment and experience to go by.
“This problem is part of everyday life fx traders, but is rarely addressed in academic research,” says Alexander Barzykin, director of the Global fx and raw materials team HSBC.
Barzykin has teamed up with two mathematicians – Olivier Guéant, full professor of applied mathematics at Université Paris 1 Panthéon-Sorbonne, and Philippe Bergault, postdoctoral researcher in applied mathematics at École Polytechnique – to correct this.
In a paper published earlier this month on Risk.net, they define the choice between internalization and externalization as an optimization problem where the state variable is the market maker’s inventory. Their model uses market parameters such as volatility and customer trading activity in response to pricing to make the optimal choice. The market maker has full control over the prices offered to clients and its trading activities on external trading venues. The underlying fair price that informs customer bids is modeled as Brownian motion and influenced by market impacts.
An innovative feature of the model is the segmentation of customers into tiers, which makes it possible to more accurately capture their reaction to price changes. “In this document, we offer a way to tier clients purely quantitatively by analyzing their trade flow. And then we show how to integrate these layers into the model,” says Barzykin. The client tiers can be formed in different ways. The paper categorizes customers into two tiers based on their sensitivity to price changes. Some clients have specific positions to take and their activities are less likely to be affected by price changes, while others are more likely to act when they see an attractive price.
At a high level, the study suggests that an internalization rate of around 80% is optimal G10 Currencies, although this may vary depending on market volatility and customer flows. “Indeed, under standard assumptions on risk appetite and daily turnover, the model confirms that this internalization is optimal on average,” says Barzykin. The result correlates with current industry practices, while the optimal risk neutralization time derived from the model was also in line with market norms.
mix approaches
The paper draws inspiration from existing research. “On the one hand we have the work of Avellaneda-Stoikov, which was very influential work on market-making strategies but focused on internalization. On the other hand, there is the Almgren-Chriss model, which looks at algorithmic execution on all-to-all platforms,” says Barzykin. “Of a fx From the trader’s perspective, bringing them together is very natural as pure internalization helps maximize spread capture but comes with flow uncertainty and hence price risk, while externalization helps control risk but with transaction costs and market impact. To manage the coexistence of requests for quotations and access to liquidity pools, we need both work.”
Bringing all of this together was mathematically complicated as client flows are discrete while liquidity pool trading is continuous.
“When you mix discretely and continuously, you have to deal with partial integral differential equations, which are not very friendly,” says Barzykin, “but Philippe and Olivier are brilliant mathematicians, so we took on the task.”
The obvious use case for the model is to determine the optimal electronic pricing and hedging strategy for fx Market makers, but Barzykin says that “the qualitative understanding is no less valuable – the model clearly answers the dilemma of whether to hedge or not”.
The research could lead to further breakthroughs. Optimization problems like this can be difficult to solve with model-free deep learning approaches due to the large number of variables that require a large amount of training data. Parametric models like the one presented in this article are better suited for this task, but once developed they can also support the training of deep lending engines. “It can provide a realistic benchmark that you can simulate enough times to train the neural network before embarking on a model-free journey,” says Barzykin.
The journey continues for Barzykin. So far, the model has only been applied to a single currency pair, but he has already worked with Guéant and Bergault to extend it to multi-currency portfolios. The results of this work will be published shortly.
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