# What’s the right price limit for an algo?

## BestX assesses the different impacts a price limit can have on FX algo performance

In algorithmic execution, the price limit serves as the stopping criterion. The algo ceases operation once the price exceeds this limit, enabling users to manage foreign exchange algo execution risks. However, there are no standard guidelines for users to determine the optimal price limit.

Price limits can serve as a protective shield for users during flash-crash events, such as the one that occurred on October 7, 2016, when sterling fell drastically by more than 6% within the space of two minutes before rebounding. Without a limit, algo users could potentially bear significantly higher transaction costs.

Interestingly, this problem exhibits similarities to American option pricing. In the world of option pricing, knock-in/knockout conditions are given factors, and the aim is to evaluate the option’s value. In the context of optimal algo price limit, price limits function as control variables instead of given factors. By defining the final condition of the utility functions, we can represent this problem as a stochastic control/optimal stopping problem. The performance to the arrival price could be expressed as:

Given a concave Boundary Utility function:

Solving this problem numerically would require making substantial assumptions about the volatility process, and the optimal limit would become a dynamic function, dependent on past prices, current inventory and current volatility conditions. While this might be appealing for an algo designer, it poses challenges for buy-side FX users in their routine tasks.

However, there is an alternative statistical approach to this problem. The optimal price limit can be bounded by the following two scenarios:

1. If the price limit is set too far, it will never be triggered, hence offering no price protection.
2. If the price limit is set too close, it will be frequently activated, thereby increasing the risk of incomplete execution.

Performance can be further analysed based on different scenarios, such as whether the limit is engaged at the start, not set at all, set but not engaged, or set and engaged. As shown in the chart below, these different conditions yield different results.

For instance, consider the GetDone algorithm, which is designed to acquire liquidity as quickly as possible. This rapid approach could potentially disrupt the market unexpectedly. Therefore, it is beneficial to establish a limit for the GetDone algorithm in all situations, as it provides a safety measure against potential market disruption.

Intuitively, a fast-executing algorithm could significantly impact the market, so having a limit setting overall is advantageous. This understanding allows users to make more strategic decisions about setting price limits, thereby reducing the risks associated with algorithmic execution.

We can delve deeper into the analysis of performance based on the settings of the limit distance. For example, from the chart below, the optimal price limit for interval algorithms is set between 0.8 and 1.0 times the daily volatility from the arrival mid. This analysis provides a more precise guideline for setting price limits.

When it comes to opportunistic algorithms, which are positioned towards the more sophisticated end of the spectrum, adding a limit doesn’t seem to enhance performance.

On the other hand, GetDone algorithms paint a different picture. As these algorithms fall on the more aggressive side of the spectrum, setting up a limit seems to offer overall benefits.

This highlights the importance of understanding the specific characteristics of each algorithm when considering the implementation of price limits.

It is important for readers to understand that a balance must be struck between order completion and price protection. The grey bar in the chart represents the proportion of the algo order that has been fully completed. We can further dissect the performance by looking at different scenarios where orders have been filled to varying degrees, as illustrated in the chart below.

By taking these insights into account, users can make more informed decisions regarding price limit settings, reducing the risks associated with algorithmic execution.

Yangling Li is the head of analytics and quantitative research at transaction cost analysis provider BestX. The analysis is based on a recent paper published by BestX titled “Do limits improve algo performance?”. The paper is co-authored by Li and Sait Oztruk, quantitative researcher and developer at BestX.

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