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accepted Closed-form formula for approximate maximum duration of a bond?
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comment Modified Durations of Different Noncallable Bonds and function of Maturity
The horizontal asymptote will always be at duration=(1 + 1/i) where i is the current market interest rate expressed in proportion terms (e.g. i=.05 for a 5% rate).
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comment Modified Durations of Different Noncallable Bonds and function of Maturity
See the answers to this question about how to calculate the maximum duration for some more references and graphs: quant.stackexchange.com/questions/1624/…
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revised Closed-form formula for approximate maximum duration of a bond?
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revised Closed-form formula for approximate maximum duration of a bond?
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revised Closed-form formula for approximate maximum duration of a bond?
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comment Closed-form formula for approximate maximum duration of a bond?
Thanks for this. I'm still sorting through all this, but in re-reading both the Pianca paper and the Hawawini paper I am starting to realize that my previous lack of progress on this issue results from my assumption that the closed-form formulae for duration were approximations. By contrast, Pianca seems to use them as though they are exact. I'll have to work through the derivations and figure out whether they are, in fact, exact. If so, I can likely avoid the whole iterative algorithm and just go directly from maturity to duration.
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revised Closed-form formula for approximate maximum duration of a bond?
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comment Closed-form formula for approximate maximum duration of a bond?
These aren't actual bonds. This is portfolio generation, which is why working backwards is required. The idea is that you given that you already have a collection of (n-1) bonds in a portfolio with duration d and a target portfolio duration D, what is the maturity of the $n^{th}$ bond you should purchase to move the new d to D.
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answered Closed-form formula for approximate maximum duration of a bond?
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asked Closed-form formula for approximate maximum duration of a bond?