Another possibility of a extreme sport is rafting on the river Mzymta that comes from Krasnaya Polyana, where the "mailinki (small) Mzymta" meets the "bolshaya (big) Mzymta". The river is known to be very changing. One moment it's a peaceful mountain creek and suddenly (after hard rain in the mountains) is swells up to be a all destructive force of nature, blasting it's way to the Black Sea near Sochi - Adler. In the week before our visit to the area 17 people drowned in a rafting accident, so do inform yourself about the present and recent weatherconditions before joining a rafting tour and do not be as recklless as some Russians like to do to look tough (but actually only show lack of braincapacity). Rafting is however a great way to experience the canyon from within and feel the power of the mountain river Mzymta.
Equipment: For rent in excursion tours.
If you like to fly, here's an option that will not cost you a fortune. In the European alpes, as well as - no doubt - in various other places in the expensive "Western" world, prices to go parapenting exceed to hundreds of euro's. Here one can enjoy flying down the mountain for just a lousy 70 euro ... including the ticket to go up the mountain by cablelift (which is alone already around 25 euro). The parapenting gliders are all experts and I am referring to a duo-jump, so you need not worry about having a lisence or experience to do it yourself.
Equipment: For rent at location in Krasnaya Polyana.