We propose a method for estimating disparity confidence intervals in stereo matching problems. Confidence intervals provide complementary information to usual confidence measures. To the best of our knowledge, this is the first method creating disparity confidence intervals based on the cost volume. This method relies on possibility distributions to interpret the epistemic uncertainty of the cost volume. Our method has the benefit of having a white-box nature, differing in this respect from current state-of-the-art deep neural networks approaches. The accuracy and size of confidence intervals are validated using the Middlebury stereo datasets as well as a dataset of satellite images. This contribution is freely available on GitHub.