What is the Delta of an at-the-money binary option with a payoout $0$ at $<100$ dollars, and payout $1$ at $>100$ dollars, as it approaches expiry?
This is from a sample interview exam. I understand that Delta essentially measures the change in the derivative price relative to the change in the asset price, as trading on the open market.
How do I actually go about computing Delta for a particular situation like the one above? I've been unable to find a formula for it on Google which is a bit weird? My naive guess is that the answer should be 0.5 but I'm not sure why?
Answer
If it wasn't clear from the previous answers, the answer they want is that the delta becomes infinite. That's because a tiny move in the stock will change the payout by $100 so your delta hedge must be enormous.
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