Whenever we replace an order, we lost priority since we are added to the end of the queue. If we dont replace an order, there is an obvious chance that we might get picked. There are other situations possible, when we replace deeper back and forth in the book and keep losing priority. Is there any literature which discusses this trade off and what is an optimal way of replacing orders?
they are now plenty of academic resources to address the point of interacting with liquidity via limit orders:
- Stochastic control is the best way (it's optimal!) but you need a model of liquidity dynamics: Charles-Albert Lehalle, Othmane Mounjid, and Mathieu Rosenbaum. "Optimal liquidity-based trading tactics." Stochastic Systems 11, no. 4 (2021): 368-390.
- the Queue Reactive Model is probable the best suited that for: Huang, Weibing, Charles-Albert Lehalle, and Mathieu Rosenbaum. "Simulating and analyzing order book data: The queue-reactive model." Journal of the American Statistical Association 110, no. 509 (2015): 107-122.
- if you want a model free version, use Reinforcement Learning (RL) and look in the examples of this paper: Mounjid, Othmane, and Charles‐Albert Lehalle. "Improving reinforcement learning algorithms: towards optimal learning rate policies." Mathematical Finance (2019).
If you want to focus more on the price at which you post than on the queuing strategy, you may have a look at this paper: Laruelle, Sophie, Charles-Albert Lehalle, and Gilles Pagès. "Optimal posting price of limit orders: learning by trading." Mathematics and Financial Economics 7, no. 3 (2013): 359-403. It is a RL approach to guess the best price by trial and error.
And if the most important for you is the sequence of quotes you will offer during the day, having in mind to finish the day with zero inventory, this one is for you: Guéant, Olivier, Charles-Albert Lehalle, and Joaquin Fernandez-Tapia. "Dealing with the inventory risk: a solution to the market making problem." Mathematics and financial economics 7 (2013): 477-507.
- An order loses time priority when its replace size is higher than current size at same price.
- An order does not lose time priority when replace size is lower or equal to earlier size at same price.
Build a probabilistic model of order being filled at various price depths and sizes. Doing this for a single instrument uncorrelated is comparatively simpler, however for correlated instruments like options of same underlying is harder.
You may refer to the following -
Guo, Xin, Zhao Ruan, and Lingjiong Zhu. "Dynamics of order positions and related queues in a limit order book." arXiv preprint arXiv:1505.04810 (2015).
Moallemi, Ciamac C., and Kai Yuan. "A model for queue position valuation in a limit order book." Columbia Business School Research Paper 17-70 (2016).
There is no easy answer when it comes to deciding whether or not to replace an order. Each situation is unique and must be evaluated on its own merits. However, there are some general guidelines that can be followed in order to make the best decision possible.
Whenever possible, try to avoid replacing an order. This is because each time an order is replaced, you lose your place in line and are added to the end of the queue. This can obviously have a negative impact on your chances of getting picked.
There are other situations where replacing an order may be beneficial, such as when you are deeper in the book and have a better chance of getting picked. In these cases, it is important to weigh the pros and cons of replacing an order before making a decision.
The best way to evaluate whether or not to replace an order is to consult with literature on the subject. This will help you to understand the trade-offs involved and make the best decision possible.