Coupled chain ladder that corrects the paid and the incurred triangle at the same time using their ratio, removing the gap between the ultimates the two triangles produce separately.
A paid triangle and an incurred triangle describe the same book and should converge to the same ultimate. Run separately they almost never do, and the actuary arbitrates by hand. Gerhard Quarg and Thomas Mack showed in 2004 that the gap is not noise: when an accident year's paid-to-incurred ratio sits above its average, future paid development is systematically lower and future incurred development higher. Munich chain ladder exploits that correlation by correcting each development factor by a term proportional to the paid-to-incurred residual. The two projections then converge mechanically. The method needs two consistent triangles and a stable definition of incurred: if case reserving practice changed mid-period, the correlation it measures is the correlation of the practice change, not of the risk.
Motor bodily injury book as of December 31, 2025. Chain ladder on paid returns a 112M EUR ultimate, on incurred 127M EUR, a 15M EUR gap that three successive closings had failed to close. Munich chain ladder brings the two projections to 119M and 121M EUR, and the 2M EUR residual gap fits inside the Mack interval.
MCL, Munich chain-ladder, chain ladder couplé payé charge