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?

  • $\begingroup$ Your T-bill yield quote is probably already annualized using a 360 day year. investopedia.com/articles/bonds/08/… $\endgroup$
    – user508
    Commented 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
    Commented May 18, 2011 at 12:46

1 Answer 1


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


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.