Swaps and Swaptions

Can anyone provide a quick summary on swaps and swaptions and how to compute them? I’ve read through it twice and thought I understood it until I got to the questions and failed them.

I haven’t written anything about swaptions yet, but here are a couple of articles I wrote on plain vanilla interest rate swaps:

Maybe they’ll help.

Here’re the quick formula for swaptions:

Swaption Payoffs : (market rate – strike rate) x time factor to unannualize x notional $ principle

Swaption valuation : PV ( Swaption Payoff , same payoff for all periods), discount back to PV using different discount factors (for different forward periods)