what tasks do trading interns want to do?

Don't give work for the sake of work. Either it should be value for them or value for you, and preferably both. I worked with a guy many moons (1 summer ago), and something he did after so many years of having interns pass through is that he came up with little projects at the very beginning that necessarily forced you to ask questions/learn about the business and learn the tools that the team used in a low risk way. So he would tell me go produce a report on our historic pipeline flows using xyz software and go tell me what stands out. I had to learn the tech and then I had to go find what I should be looking for that stands out (learn the business/relevant metrics) and then it would force me to ask questions. This would be something easy to do, and it helps build credibility. From then on he knew he could trust me to do more useful analysis with greater independence. Also low stakes daily briefings for info you like to have, but don't necessarily have the time for. So I would produce reports on outages every morning and eventually built a tool to automate it. The key in all of this is it has to be of use to you, so even though the daily briefing was a bit of a chore to put together it still felt like I wasn't a useless appendage. You don't need them doing things that could cost the business substantial amounts of money if they fuck up, but it's not like we are dumb enough to not recognize when shit isn't valued. My actual boss that summer had me do one true deliverable and I knew it was never read, since it was a weekly email with updated spreadsheets I had done, and the email system told me how many people on the list I sent it to would open the actual file (zero). I wouldn't mind this if it forced me to learn the business, but instead it was me copying and pasting numbers from a report we get and updating the graphs associated with it. Probably not so coincidentally he never really took the time to answer questions I had about what our team did. Don't be that boss. Also don't underestimate the value of just letting them observe you and pick your brain. Hopefully you can find work that can help you and the intern, but if you feel you have to create work at least do something that forces them to learn something new.