Quantum algorithm for calculating risk contributions in a credit portfolio

Abstract: Finance is one of the promising field for industrial application of quantum computing. In particular, quantum algorithms for calculation of risk measures such as the value at risk and the conditional value at risk of a credit portfolio have been proposed. In this paper, we focus on another problem in credit risk management, calculation of risk contributions, which quantify the concentration of the risk on subgroups in the portfolio. Based on the recent quantum algorithm for simultaneous estimation of multiple expected values, we propose the method for credit risk contribution calculation. We also evaluate the query complexity of the proposed method and see that it scales as $\widetilde{O}\left(\sqrt{N_{\rm gr}}/\epsilon\right)$ on the subgroup number $N_{\rm gr}$ and the accuracy $\epsilon$, in contrast with the classical method with $\widetilde{O}\left(\log(N_{\rm gr})/\epsilon^2\right)$ complexity. This means that, for calculation of risk contributions of finely divided subgroups, the advantage of the quantum method is reduced compared with risk measure calculation for the entire portfolio. Nevertheless, the quantum method can be advantageous in high-accuracy calculation, and in fact yield less complexity than the classical method in some practically plausible setting.