Matching quantiles estimation

Motivated by a backtesting problem for counterparty credit risk management, we propose a new Matching Quantiles Estimation (MQE) method, for selecting representative portfolios. An iterative procedure based on the ordinary least squares estimation (LSE) is proposed to compute the MQE. The convergence of the algorithm and the asymptotic properties of the estimation are established. A new measure and an associated statistical test are proposed to assess the goodness-of-match. The finite sample properties are illustrated numerically by both simulation and a real data example on selecting a counterparty representative portfolio. The proposed MQE also finds applications in portfolio tracking, which demonstrates the potential usefulness of combing the MQE with the LASSO.