Re: constant forward in yield curve for intermediate quotes

Posted by Peter Caspers-4 on
URL: http://quantlib.414.s1.nabble.com/constant-forward-in-yield-curve-for-intermediate-quotes-tp16770p16771.html

André,

the *instantaneous* forwards f(t) should be constant between the
curve's pillar dates when interpolating loglinear in discount.
Discrete forwards will vary slightly though, because

(a) they are simply compounded, so equal to ( exp( int_s^t f(u) du )
-1 ) / (t-s) which is equal to f(u) only up to first order if f(u) is
constant on [t,s], assuming equal daycounters between the curve and
the discrete forward convention, or at least a pair of daycounters
with constant ratio (t-s) / (t'-s') for all dates possible

(b) they may have a different day counter than the curve so int_s^t
f(u) = f(u)*(t-s) != f(u)*(t'-s') (again for f(u) constant on [t,s])
and (t'-s') / (t-s) may not be constant for different dates, too -
even if the discrete forward would be computed using continuous
compounding; (b) applies at least for certain day counter
combinations, but not for the "usual" ones in this situation like
Act/365Fixed, Act/360.

All this is of course independent of QuantLib. Is that what you meant ?

Best regards
Peter

On 11 August 2015 at 11:12, André de Boer <[hidden email]> wrote:

> Hi,
>
> When using
>
> boost::shared_ptr<YieldTermStructure> swapTermStructure(
>                                 new PiecewiseYieldCurve<Discount,LogLinear>(
>                                 settlementDate, depoSwapInstruments,
>                                 termStructureDayCounter,
>                                 tolerance));
>
> in constructing a yield curve with quotes t = 1 ... 10, 12, 15, 20,
> 25, 30, 40 and 50 years, the forward rates are not constant for the
> intermediate years. How to accomplish this?
>
> Regards,
> André
>
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