Do Thunderbolt to Display Port cables exist? Is there any  such cable? I'm trying to connect a monitor with display port connector to a MBA with Thunderbolt port. I know I can use a Display port to Mini-display port cable but I'm wondering if there is any Thunderbolt to Display Port cable so that I can get a better resolution.
There can be no such thing.

Thunderbolt is an active technology, Display Port is passive.
Adding the required circuitry to one end of such a cable would be pointless - it needs both ends to work.

Edit: Now I read your question again…

You have a Thunderbolt machine &amp; a Display Port monitor…

That's Thunderbolt to Display Port not Display Port to Thunderbolt.

In which case DP to DP would be sufficient; the Thunderbolt circuitry would simply be inactive if you used Thunderbolt to Thunderbolt.
Display Port &amp; mini-DP are the same thing, but different sizes.