We describe a new framework for modeling collateralized exposure under an International Swaps and Derivatives Association Master Agreement with a Credit Support Annex. The proposed model captures the legal and operational aspects of default in considerably greater detail than the models currently used by most practitioners while remaining fully tractable and computationally feasible. Specifically, it considers the remedies and suspension rights available within these legal agreements, the firm's policies in availing itself of these rights and the typical time it takes to exercise them in practice. The inclusion of these effects is shown to produce significantly higher credit exposure for representative portfolios than do the current models. The increase is especially pronounced when the dynamic initial margin is also present.