There are 3 options tax-wise.
If you host international students as an ongoing trade or business where you goal is to make a profit, you can report the stipend as self-employment income and deduction your expenses on schedule C. I expect this is not a legally sustainable position for most host families.
You can report this as a rental, as if you were renting a room in your home to a stranger to earn money. You report the stipend as residential rental income goes on schedule E. You can apportion part of your mortgage interest, utilities and other expenses to the renter. You can't deduct a loss unless you are renting at fair market rates, which means the best you can do is break even and neutralize the taxable income. However, this is not widely accepted in my limited research and you may want to run it by a tax advisor. Also, if you report your home as a rental, you will have to keep track of depreciation and you will have a taxable gain when you sell the home even if you normally would qualify for the exclusion. It may be more trouble than its worth.
You report the income as miscellaneous other income on line 21. You don't deduct any expenses as business or miscellaneous expenses. This is because, if you aren't reporting rental income, then there is no method under the tax law to divide your cost of living since you would pay the same for your rent or mortgage, and almost the same for utilities, whether or not you had an exchange student. You can take up to $50 per month as deduction for a contribution to charity. There are a number of additional documents you must send to the IRS in this case, start here on page 4. <a rel="nofollow" target="_blank" href="
https://www.irs.gov/pub/irs-pdf/p526.pdf">https://www.irs.gov/pub/irs-pdf/p526.pdf</a>
While it is true that your expenses may exceed your stipend, that does not give you an automatic right to claim expenses and zero out the income. It's part of having host kids -- if you really want to zero your expenses and make money, you would need to open a hostel or a B&B. Claiming the income as rental income rather than as "other income" gives you an ability to deduct more of the expenses but may also create unwelcome issues later on.
