Topic Models have been reported to be beneficial for aspect-based sentiment analysis. This paper reports the first topic model for sarcasm detection, to the best of our knowledge. Designed on the basis of the intuition that sarcastic tweets are likely to have a mixture of words of both sentiments as against tweets with literal sentiment (either positive or negative), our hierarchical topic model discovers sarcasm-prevalent topics and topic-level sentiment. Using a dataset of tweets labeled using hashtags, the model estimates topic-level, and sentiment-level distributions. Our evaluation shows that topics such as ‘work’, ‘gun laws’, ‘weather’ are sarcasm-prevalent topics. Our model is also able to discover the mixture of sentiment-bearing words that exist in a text of a given sentiment-related label. Finally, we apply our model to predict sarcasm in tweets. We outperform two prior work based on statistical classifiers with specific features, by around 25%.