thanks you all for sharing your opinions.
This is very interesting rawand, yes please post more when they answer !
I actually was wrong when at first considered return rates were fixed. The guy from tradologic said they manage the risk by managing the price of their options. Translated to binaries, the parameter they can adjust is the return rate. I looked at it as fixed per broker/per asset/expiration time, but they can (and probably do) change it whenever they want.
If we bring the first example back and genelarize it from the broker perspective, we get something like this :
raw profit = Sum,i,k(
amount bet (i)
* (1 - asset return rate (k) when out of the money) * is bet (i) out the money
* (0 - asset return rate (k) when in the money ) * is bet (i) in the money
He just observes amount_bet(i), is_bet_in_the_money_(i) / (out) (=rate at which customers win or lose) and controls the two return rates. If he has enough client, those distributions will likely be gaussian (if not that doesn’t change the problem). He can make the assumption that, let’s say next week bets, will be disttributed the same as what observed until now. If distributions are gaussian (or any symmetrical) he simply use means to calculate what return rate will assure him positive profit.
So yes, he not only makes money as long as return rates respect the expected ratio of amounts bet by options winners and losers, but also knows how much he’ll make.
Now the other aspect many of us are interested in : what if the rare case of a more-enough-than-average-trader occurs ? The broker will want to know the probability of a one his client winning millions (especially without having the symetric client who lost same millions).
That’s just the study of marginal cases.
If the distributions are known, you can easily calculate the probality. He may also choose to insure himself against those cases. He may just choose not to be honest and not to pay this lucky client.
In conclusion : the broker controls easily how much money he makes out of binaries. Clients making money is then not a problem. BUT the rare client making too much money is a problem for him. The threshold of what if marginal depends on brokers, and it’d be very interesting to learn more about those considered by brokers.