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I. Clark introduces the concept of volatility time in Foreign Exchange Option Pricing under which the implied volatility should be interpolated in time with the formula below: enter image description here

where w is a weight function. He assumes that w is equal to 1 for any business day (Monday to Friday) and 0 for weekends. I'm wondering how could I get a more accurate estimation of w for each day based on historical data?

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As explained in the chapter 4.4 of I. Clark, you can estimate the weights by using the typical trading volumes.
You can give more weight for dates with bigger trading volume which is logical.

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