Let's say we have an option with underlying stock X and 2 years until maturity. We work out its volatility from X's historical prices across 3 trading years (756 days). To price the option, I can use Black-Scholes and feed in the parameters - but what if I want to also find the options price on the previous days that we got X's historical prices from?
Am I correct in assuming that every day we go back from today our time to maturity will increase by 1/252 (aka 1 trading day)? Does this mean that we have to recompute the volatility every day we go back to exclude the "future" days?
So day 1 (today) uses our initial time to maturity
T and volatility; day 2 (yesterday) uses
T-(1/252) as the time to maturity and recomputes the volatility to exclude day 1; and so on...
Highly appreciate any help, thanks.