• Corpus ID: 250280009

A cross-border market model with limited transmission capacities

@inproceedings{Milbradt2022ACM,
  title={A cross-border market model with limited transmission capacities},
  author={Cassandra Milbradt and D{\"o}rte Kreher},
  year={2022}
}

• Cassandra Milbradt, D. Kreher
• Published 5 July 2022
• Mathematics

We develop a cross-border market model between two countries in which the transmission capacities that enable transactions between market participants of different countries are limited. Starting from two so-called reduced-form representations of national limit order book dynamics, we allow incoming market orders to be matched with standing volumes of the foreign market, resulting in cross-border trades. We introduce a microscopic model that consists of two bid and ask price processes, four queue length processes that describe the number of unexecuted limit orders at the best bid and ask prices, and a capacity process. The latter counts the net number of executed cross-border trades over time. Since the transmission capacities in our model are limited, our model alternates between regimes in which cross-border trades are possible and regimes in which incoming market orders can only be matched against limit orders of the same origin. If the size of an individual order converges to zero while the order arrival rate tends to infinity, we derive a continuous-time limit approximation of our microscopic market dynamics. If transmission capacities are available, the limit process behaves as follows: the volume dynamics is a four-dimensional linear Brownian motion in the positive orthant with oblique reflection at the axes. Each time two queues simultaneously hit zero, the process is reinitialized at a new value in the interior of $\mathbb{R}^4_+$. The capacity dynamics turns out to be a bounded continuous process of finite variation. Since the tick size in our model is constant, the price dynamics follows a two-dimensional pure jump process with jump times equal to those of the volume approximation. The usefulness of the ability to transact across borders is illustrated through a simulation study.