Re: Forwards

Posted by Ferdinando M. Ametrano-2 on Apr 24, 2002; 11:50am
URL: http://quantlib.414.s1.nabble.com/Forwards-tp2011p2014.html

At 03:44 PM 4/24/2002 +0100, Luigi Ballabio wrote:
>>The QuantLib term structure interface allows for modelling of discount,
>>zero rate or forward rate based curves. There is no preference towards forward.
>No, the question was: in case of forward rates, why instantaneous ones and
>not finite-time ones?
>[...] what if I want to model the forwards from t1 to t2 and derive
>discounts, zeroes and instantaneous forwards from them?
There is not a real difference between instantaneous and finite-time forwards.
In the following with NxM, M>N I means a forward rate agreement (FRA) to
enter into a M-N months deposit N months from today.
If you're thinking about a yield curve representation in terms of [0x3,
3x6, 6x9, ...] FRA this is equivalent to have a piecewise constant
instantaneous forward curve with nodes [0,3,6,9,...]
If you're thinking about a yield curve built from something like [0x3, 1x4,
3x9, ...] this is equivalent to a [0x1, 1x3, 3x4, 4x9, ...] FRA strip, i.e.
a piecewise constant instantaneous forward curve with nodes [0, 1, 3, 4, 9,
...]
When you settle on the instantaneous forward parametrization there are no
problem to calculate whatever FRA. This is not true if you parametrize your
curve as a FRA strip, e.g. [0x1, 1x3, 3x4, 4x9, ...], since in this case
there are many plausible combinations of intermediate FRAs, e.g. the (1x2,
2x3) pair

Maybe I'm missing something here, but when it comes to internal yield curve
representation I know of discount, zero, instantaneous forward, and par
rates only.
Always willing to learn something more ....

>The point being: once you model discounts, zero rates or instantaneous
>forward rates, of course you can write a method returning forwards from t1
>to t2.
I committed such a method in the CVS, along with some code refactoring in
order to make the subject clearer.

What was poorly documented before is that in the TermStructure interface
all rates are assumed to be annual (time measured in years) continuos
compounding.
This requirement is not the best choice, but to change it would be a lot of
work since it's a pervasive assumption.
This means that TermStructure::forward(Date d1, Date d2) will not return a
FRA quote, since FRA are usually quoted with simple compounding.

Another point that I want to make clear is that I'm talking about internal
yield curve parametrization. There is no problem in using FRA to calibrate
your favorite yield curve parametrization, whatever your favorite is

ciao -- Nando