Is it permissible for him to set up a business in the place where they sell binary options to give indications as to whether one should buy or sell?

Praise be to Allah.

1. The ruling on trading in binary options

It is not permissible to trade in binary options, because the thing that is the subject of the contract is not property or a benefit, and it is not wealth that it is possible to replace with something else – which is a condition of a transaction being valid. Rather the subject of the contract is the mere right to buy or sell at a set price. So what is being sold is the option itself, and this is something that it is not permissible to buy or sell.

Moreover, this contract involves ambiguity and gambling.

See the answer to question no. 258619, in which you will find the statement of the Islamic Fiqh Council regarding this topic.

2. Offering expertise and advice in the place where binary options are offered for sale

What we understand from your question is that you want to offer your expertise and advice in the place where binary options are offered for sale, in return for payment. This is haraam, because it is helping in selling something that is haraam. Allah (may He be exalted) says (interpretation of the meaning):

“And cooperate in righteousness and piety, but do not cooperate in sin and aggression. And fear Allah; indeed, Allah is severe in penalty”

[al-Maa’idah 5:2].

It is haraam to sell binary options, and it is also haraam to help others in that by offering advice as to when to buy and sell. Any income earned from that is also haraam.

It is not permissible for a person to commit a haraam action in order to help the needy; rather the fact that it is haraam is connected to two things: the sin and the money earned through it. Supposing that you can get rid of the money, how will you get rid of the sin?

Perhaps you can find a permissible field in which you can use some of your expertise.

And Allah knows best.