Approaching Collateral Optimization for NISQ and Quantum-Inspired Computing

TL;DR

This paper formulates collateral optimization as a large-scale combinatorial problem, proposing MILP and QUBO models to explore hybrid quantum approaches, supported by small-scale computational tests and literature review.

Contribution

It introduces MILP and QUBO formulations for collateral optimization, aiming to leverage quantum computing techniques and assesses their potential through initial computational experiments.

Findings

QUBO formulation enables quantum-inspired optimization approaches.

Small-scale tests show potential for performance improvements.

Survey of recent literature highlights alternative optimization methods.

Abstract

Collateral optimization refers to the systematic allocation of financial assets to satisfy obligations or secure transactions, while simultaneously minimizing costs and optimizing the usage of available resources. {This involves assessing number of characteristics, such as cost of funding and quality of the underlying assets to ascertain the optimal collateral quantity to be posted to cover exposure arising from a given transaction or a set of transactions. One of the common objectives is to minimise the cost of collateral required to mitigate the risk associated with a particular transaction or a portfolio of transactions while ensuring sufficient protection for the involved parties}. Often, this results in a large-scale combinatorial optimization problem. In this study, we initially present a Mixed Integer Linear Programming (MILP) formulation for the collateral optimization problem, followed by a Quadratic Unconstrained Binary optimization (QUBO) formulation in order to pave the way towards approaching the problem in a hybrid-quantum and NISQ-ready way. We conduct local computational small-scale tests using various Software Development Kits (SDKs) and discuss the behavior of our formulations as well as the potential for performance enhancements. We further survey the recent literature that proposes alternative ways to attack combinatorial optimization problems suitable for collateral optimization.