Re: Forwards
Posted by Luigi Ballabio-4 on Apr 24, 2002; 2:29pm
URL: http://quantlib.414.s1.nabble.com/Forwards-tp2011p2015.html
At 7:48 PM +0200 4/24/02, Ferdinando Ametrano wrote:
>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.
Of course there is not.
There is no real difference between forwards and discounts, either:
given one curve you can calculate the other and viceversa :)
>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
Not true. You don't specify your curve as a FRA strip only: you give
a FRA strip *and* a functional form. A simple example which might not
make sense but gives the idea is: you store the deposit strip
[0x1,0x3,0x6,0x9,0x12] and assume that the 0xT rate is interpolated
linearly in T. Given this functional form, you can calculate whatever
FRA. And in this case, it would be discounts, zero yields, and
instantaneous forwards which would depend on the 0xT rates.
Also in the case of our curve, you give a number of instantaneous
forward at the nodes *and* a functional form (piecewise flat). The
former without the latter would not be sufficient.
>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.
On this point I can agree. But there are more things in heaven and
earth, Horatio, than are dreamt of in your philosophy...
>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.
That depends on what we decide (and on the name of the method. I
wouldn't overload forward() to give different kind of forward rates)
Bye,
Luigi
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