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Black-Scholes requires volatility estimated in trading days. How does this affect other parameters? Specifically, should the time-to-expiration also be in trading days? And how does this affect the risk-free interest rate?

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you want to be consistent. Whatever annualization factor you use, apply it across all inputs equally. There is no recipe for BS which exact trading day adjustment to apply. BS is a framework with inputs left to its user. You are to decide which inputs to feed into BS. –  Matt Wolf Apr 24 '13 at 8:48
    
Don't forget that historical estimates of volatility are, in general, smaller than market-implied volatilities. –  Brian B Apr 25 '13 at 13:24
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up vote 3 down vote accepted

I remember this discussion here: http://www.wilmott.com/messageview.cfm?catid=3&threadid=62227

You should absolutely match your convention for time to expiration to the convention you used for calculating volatility. There seems to be other ways to proceed, as modifying the volatility to match your convention but I don't really see the point in using them.

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the convention for most market makers of options is to use calender time. it is also the convention in data one gets from options data vendors. another way to see this is that market makers will fade their bids near the close on a 'normal' friday for fear of holding inventory ahead of the weekend, since it is a crap shoot whether the pick-up in vols on Monday morning will offset the time decay from a ho-hum weekend. all this holds on average.

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