A SCH C business can only claim a home office deduction, only if that business has the income on the SCH C to deduct the allowed costs from. If the SCH C business doesn't have the income, you can "claim" the home office. But no deduction can occur from zero business income reported on the SCH C.
Now a SCH C is for "earned" income. What I don't know, because I'm not a trader and don't know anyone who is, is if income from playing wall street is earned income, or passive income. My wild guess, based on no facts what-so-ever is that it's passive income. The only thing reported on SCH C is "earned" (sometimes referred to as active) income. That income would be paid to you in cash, or reported to you on a 1099-MISC box 7. That's pretty much all that counts for SCH C income.