# Does the Black-Scholes formula work when unit of time is in hours?

In the Black-Scholes formula, the unit of time is usually in years from what I understand. An online calculator I found allows the users to input the time in days and years.

Would the formula still be accurate if I were to plug in say 1 hour for the time variable, by first converting it to years, given that 1 hour is roughly 0.000114155 years? I would assume yes, but the reason I am asking is because of this case scenario that I found with the above calculator. Given the following parameters, the calculator returns a call value of $7.81. However, when I change the time units to years, and plugin the above converted value of one hour to years, the call value drops to$7.00. Why is this the case? Shouldn't a dramatic move increase the price for a call option if it happens in a shorter period of time versus if it takes longer to happen?

• 255/248 is not the same moneyness for 1 hour versus 1 day or 1 year. That is why the results seem counterintuitive.
– user34971
Apr 2, 2020 at 16:46
• @ilovevolatility That makes sense now. So the expected call prices are accurate, but just seem counterintuitive? Could you use that method to determine the price of an option intraday? Example: I expect underlying X to move Y dollars in Z time, plug in Z time for the time to maturity, and return a theoretical call price? If not, what would be the best way to do that? Apr 2, 2020 at 16:49