Today, during my Sociolinguistics course offered by the Department of Linguistics at Hacettepe University, I had the opportunity to listen to a presentation, which was actually a progress report on a PhD study (by one of the research assistants) on: Converational Narrative.
A study on conversational narratives finds its basis within conversational analysis, yet focuses exclusively on the sections of story-telling during daily conversations. It provides a very effective insight on the functions of linguistic items and on how they convey the intended sense during conversation. The issue is very interesting and open to research.
One of the basic texts (by the esteemed W. Labov) is available here: http://www.clarku.edu/~mbamberg/LabovWaletzky.htm
For a broader account of the studies on the field, please visit: http://narrative.georgetown.edu/wiki/index.php/Conversational_narrative