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.
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$\begingroup$ 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. $\endgroup$– dm63Jul 13, 2019 at 10:27
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$\begingroup$ 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. $\endgroup$– wormeerJul 13, 2019 at 10:50
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$\begingroup$ So, in my calculations the duration equals 1 (not 1/2 - time to the fitst coupon payment).. Why is so? $\endgroup$– wormeerJul 13, 2019 at 10:56
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$\begingroup$ Shouldn’t be. Let the first coupon be c, and let all other rates move, including L(0,6) $\endgroup$– dm63Jul 13, 2019 at 11:27
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$\begingroup$ Ok. What wrong in the formula? I used the simple definition of a duration, which you can find in Wikipedia.. $\endgroup$– wormeerJul 13, 2019 at 11:47
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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 $L=L_(0,6)$.
