Up duration of a callable bond is higher than its down duration.
Why?
Price increase of a callable bond is capped by the embedded call, there is a higher chance that if will be terminated when prices increase (rates decrease). Why does it have a higher (and not lower) up-duration then?
To be honest I don’t remember much about duration from LI, only the calculation of ED. Do I misunderstand the concept of duration?
Please help me out, thanks.
The “up” and “down” refers to the interest rates, not bond prices. So to say that callable bonds have higher “up” duration means that when interest rates go up, prices fall, and the bond is less likely to be called (and more likely to run through maturity --> higher duration).
Interest rises (goes up) the price comes down. The call value becomes less. The callable bond starts to behave like an option free bond which is sensitive to changes in interest rates. (The duration is higher effectively)
When interest falls, the price rises. The call becomes more valuable. The likelihood of early call becomes high. (Negative convexity) Thus the duration is less.
Ergo, up duration is higher then down duration.
Only when convexity is negative; i.e., at low interest rates.
When interest rates are high (and the option is out of the money), up duration is lower than down duration.
Thanks to all, clear now.
Hey there Mr. S2KM ! 
I am having a difficult time finding the formulae for one-sided up and one-sided down durations. How does it differ from the effective duration formula which I understand is equal to: (Pd - Pu) / (2 x P0 x delta interest rate)?
Howdy!
Downside effective duration:
(Pd − P0) / (P0 × Δy)
Upside effective duration:
(P0 – Pu) / (P0 × Δy)
That was lightning fast !
Thank you so much !