TermStrucutue

[audetto]

Hi,

I tried to add a BondRateHelper to build a GovernmentBond Term Structure,
but I have a little doubt.

The bootstrap method in PiecewiseFlatForwar uses a 1D solver to match exactly
all the quotes I give it. I think that for bonds (the are a lot of BTPs,
40...) it is not possible to find an exact curve, but it should be better
to parametrize the curve and minimize the sum of squares of errors w.r.t
parameters...

any idea

ciao

andrea

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[Ferdinando M. Ametrano-2]

Hi Andrea

>I tried to add a BondRateHelper to build a GovernmentBond Term Structure,
yeah, it would be a long overdue addition.

>The bootstrap method in PiecewiseFlatForwar uses a 1D solver to match exactly
>all the quotes I give it. I think that for bonds (the are a lot of BTPs,
>40...) it is not possible to find an exact curve,
It is possible, but ...

>  but it should be better to parametrize the curve and minimize the sum of
> squares of errors w.r.t parameters...
Right!

The point is you can use the current _boostrap_ approach for bonds, but the
resulting curve would be very jagged, to the point that it would produce
unreliable forward rates.
At least this was what I found out 4 years ago working on the Italian Bond
curve. The main problem was with short-dated (illiquid) bond.

To overcome this problem the favorite approach for bonds is to parameterize
the curve (e.g. Nelson-Siegel, Fong-Vasicek) and minimize the errors.
Please note that to minimize price-errors wouldn't be smart, because you
should find a way to "duration-weight" the price errors. 10bp error on a 2Y
bond is not the same as 10bp error on a 30Y bond.
My suggestion would be to minimize asset swap spread, that is to minimize
the asset swap spread of each bond with respect to the yield curve you're
building.
In a perfect (liquid) world this spread should be zero.

In any case I do not consider the bootstrap approach useless: it should be
a robust approach if you only fit very liquid bonds, e.g. the May/November
BTP series, especially because those bonds can be stripped into
coupons+principal, leading to a regularly spaced series of bonds.
Last but not least I've always considered the bootstrapped bond curve a
nice fall-back to have handy.

ciao -- Nando