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in the BS model, if an option has 3 year expiration periods, and if the time of maturity of that option is calculated( periods between the grant period 2011-9-15 and exercise periods 2014-9-15 ), and another option granted by the same company very next year (2012)and can be exercised in (2015), then what would be the time period is used for these to option to the calculate the return volatility?

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In Black Scholes formula you would use implied volatility surface for given time-to maturity and strike for first option and second option respectively (check if you have this data on bloomberg or reuters)

If you don't have options available on the market for this company , then the approximation would be to use realized volatility (average, or exponentially weighted) , you should use the same vol (and same calculation period) for both cases then as it's only an approximation.

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