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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.

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    $\begingroup$ What is the aim of this historical construction? If you want to do risk analysis then you should do it differently... $\endgroup$ – Richard Nov 17 '16 at 6:47
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The simple answer is you cannot do that really... There is no plausible way to derive the implied volatility of an option in the past given the IV as of today. You would need an entire set of historical market data snapshot at the time, the spot, forward, vol surface or the vol for the particular option you want to value.

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