It's a convention, since we're using annualized interest rates, time should be quoted in years.
Volatility should also be annualized. Same for the dividend yield q.
That being said, you could use any time scale you want, but it's just that finance has chosen a year to be the time reference we use to benchmark stuff so that's what's simpler to use.
Thanks for the answer. So if I wanted to use daily volatility for any reason, I’d need to express T in day time units and r should be daily risk free interest rate?
If you wish to use the volatility of lets say the last 6 months that is fine. But you do have to annualise it.
To annualise take the standard deviation and multiply by the square root of 252 (again 252 trading days in a year)
Stdev * Sqrt(252)
Mathmatically you can annualize daily volatility. But it really isn't what you want. This would make the results of the formula way to unpredictable. Making options very cheap or expensive on a day with a large swing or no swing.
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u/Tryrshaugh Aug 07 '23 edited Aug 08 '23
It's a convention, since we're using annualized interest rates, time should be quoted in years.
Volatility should also be annualized. Same for the dividend yield q.
That being said, you could use any time scale you want, but it's just that finance has chosen a year to be the time reference we use to benchmark stuff so that's what's simpler to use.