0
$\begingroup$

I don't understand why the duration of a floating rate note equal to the time to the next coupon payment? Please, look at my calculations.

Here: P - is price at moment 0.

enter image description here

$\endgroup$
5
  • $\begingroup$ The definition of duration for these purposes is the Price sensitivity to a bump in interest rates. Try to calculate that , assuming that the first coupon has been fixed. $\endgroup$
    – dm63
    Jul 13, 2019 at 10:27
  • $\begingroup$ In my calculations first coupon is fixed and equals L_0,6. Where L_0,6 is half-year LIBOR rate, which is fixed in the moment 0. $\endgroup$
    – wormeer
    Jul 13, 2019 at 10:50
  • $\begingroup$ So, in my calculations the duration equals 1 (not 1/2 - time to the fitst coupon payment).. Why is so? $\endgroup$
    – wormeer
    Jul 13, 2019 at 10:56
  • $\begingroup$ Shouldn’t be. Let the first coupon be c, and let all other rates move, including L(0,6) $\endgroup$
    – dm63
    Jul 13, 2019 at 11:27
  • $\begingroup$ Ok. What wrong in the formula? I used the simple definition of a duration, which you can find in Wikipedia.. $\endgroup$
    – wormeer
    Jul 13, 2019 at 11:47

1 Answer 1

1
$\begingroup$

Let the first coupon be fixed at c, and consider the duration of the bond immediately thereafter. At this point $L_(0,6)$ can move. Now in your notation you should find that $$P=N(1+c/2)/(1+L_(0,6)/2)$$. Now if you calculate $(1/P)dP/dL$ you get $1/2* (1/(1+L/2))$ which is 1/2, discounted for 6 months, where $L=L_(0,6)$.

$\endgroup$

Your Answer

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

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