As can be seen in the following video, ankle pick is very dangerous. Is there a way to counter it? Is there a way to counter it when the rival holds your ankle?
Following @mattm 's proposal...
This throw in Jujutsu/Judo (where BJJ comes from) is called kibisu-gaeshi (grabbing from the outside).
As in most cases, the key is to avoid getting off-balance in the first place. In the video you linked, the kuzushi (off-balancing) is done by pressing the neck down. You automatically have to put a foot in front as you weight is shifted forwards. Pulling the arm additionally guarantees it will be the one the attacker wants it to be eventually. As you are off-balanced and the attacker increases the pressure on the neck by dropping his weight and therefore pulling the neck downwards even stronger then, you are virtually nailed in this position, i.e. immobilised long enough for him to execute the technique.
With an upright posture, your balance is centered and can be shifted on a single leg in very short time. This means your feet are too mobile and you can easily evade attempts of this technique (and many others).
One of the main points in standing grappling combat therefore is to never let your head pulled down (this is one of the things; in general: stay in upright position, not crossing feet, firm stand). It is not only a matter of balance, but also a matter of sight/awareness. To do something against this, you have to counter these tries with moving your hip under your head again and stretching the neck (i.e. with tai-sabaki - body movement/positioning).
As this movement exposes you to attacks, you should combine it with an attack with the leg, e.g. with o-uchi-gari, possibly even in combination. There are good variants of the grip out there that are working without a gi just as well.
To make a long story short, do not let the enemy get into a dominant position like this, or he has every opportunity to finish you. Your example is only one of them. If you are passive and not use his efforts (as he is open for approximation and throws backwards when trying to get there - he essentially has to put himself a bit off-balance in order to get you where he wants you!), you deserve losing.
Before MMA rants are incoming: Even with knee attacks allowed there are very similar ways to deal with this situation - the awareness has to be a different one, though.