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?
- 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).