What Atamari said is actually not entirely correct. When indexicals are involved, there is an additional layer of meaning involved, called "character", following David Kaplan (1989).
The character is a function from contexts in intensions. An intension is a function from "circumstances of evaluations" (i.e. possible worlds, situations, etc.; depending on theory) in extensions.
Character =context=> Intension =situation=> Extension
For the example, let's assume the context is such that the speaker is Peter and it is Jan 23, 4pm. The for "I am writing an exam now", we have (in paraphrases):
Character: "The speaker is writing an exam at the utterance time"
Intension: "that Peter is writing an exam on Jan 23, 4pm"
Extension: "true" (if Peter is writing an exam on Jan 23, 4pm".
This is the basic idea of Kaplans theory of indexicala. See Zimmermann 2012 for an overview and technical details.
Kaplan, David (1989): Demonstratives. In: Almond, J & Perry, J & Wettstein, H (eds.): Themes from Kaplan. OUP. 481-563.
Zimmermann, Thomas Ede (2012): Context dependency. Maienborn, C & von Heusinger, K & Portner, P (eds.): Semantics. de Gruyter Mouton. 2360-2407.