We present Recurrence with Correlation Network (RWCNet), a medical image registration network with multi-scale features and a cost volume layer. We demonstrate that these architectural features improve medical image registration accuracy in two image registration datasets prepared for the MICCAI 2022 Learn2Reg Workshop Challenge. On the large-displacement National Lung Screening Test (NLST) dataset, RWCNet is able to achieve a total registration error (TRE) of 2.11mm between corresponding keypoints without finetuning. On the OASIS brain MRI dataset, RWCNet is able to achieve an average dice overlap of 81.7% for 35 different anatomical labels. It outperforms another multi-scale network, the Laplacian Image Registration Network (LapIRN), on both datasets. Ablation experiments are performed to highlight the contribution of the various architectural features. While multi-scale features improved validation accuracy for both datasets, the cost volume layer and number of recurrent steps only improved performance on the NLST dataset. This result suggests that cost volume layer and iterative refinement using RNN provide good support for optimization and generalization in large-displacement medical image registration. The code for RWCNet is available at https://github.com/vigsivan/optimization-based-registration.