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I am looking at closed-form options approximations, in particular the Bjerksund-Stensland model.

I have run into a very basic question. How should I scale the input variables in regard to time? My assumptions would be:

  • r (riskless interest rate) should be an annual rate, so if the 3-month T-bill yields 0.03%, then I should use .12.
  • σ (variance) should be annual (and according to How to calculate future distribution of price using volatility?, variance scales with the square root of time.
  • T (time to expiration) should be in years, so expiration in 83 days would be 83/365 (=0.227397) years.
  • b (cost of carry) should be an annual rate.

Have I got that right? Are there other input variables that I will need to scale before plugging in?

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  • $\begingroup$ Your T-bill yield quote is probably already annualized using a 360 day year. investopedia.com/articles/bonds/08/… $\endgroup$
    – user508
    May 17, 2011 at 20:51
  • $\begingroup$ @user508, thank you for the correction. So when they discount my $1000 T-bill, I should expect to get 7 or 8 pennies each 3 months. (I'm glad it's electronically deposited, lest the postage exceed the check.) $\endgroup$
    – rajah9
    May 18, 2011 at 12:46

1 Answer 1

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Yes, that's correct.
(use the same time unit for all of the parameters)

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