Algorithms for Order Matching in Securities Lending

Abstract: Securities Lending is a significant part of the financial industry. One important part of the securities lending business is how to match different lending and borrowing orders to maximize profits as a middle man. However, order matching is not always as straightforward as it may seem. It is a very simple problem until you introduce the fact that some lenders and borrowers have a minimum quantity of shares for a stock they want to trade. In this paper, we have created two main algorithms that solve this problem, and one combined algorithm that uses the strengths of both algorithms. The result is that it is possible to automate the order matching process with these algorithms. With real-world data from Nordea, there is no problem using a brute force approach to solve the problem optimally in almost all cases. In the few cases where the brute force approach is too slow, a greedy approach can be used to solve the problem very quickly, even if there is a lot of orders with a minimum quantity. The trade-off is that an average error of 0.02% from the optimal solution is introduced. However, this is small enough that for most real-world applications it is better to have a good solution fast than an optimal solution slow.