[Quantlib-users] Modifying ExponentialSplinesFitting class for FittedBondDiscountCurve

[<da...@el...>]

Hi everyone,

 

I've made some mods for my own use to the ExponentialSplinesFitting class,
and before I go ahead and submit a pull request, I'd appreciate some initial
feedback.



The form of the discount function for the exponential spline fit is: df(t) =
sum( b(i) exp -i.kappa.t ) for i = 1 to N.

Where b(i) and kappa are the variables used to fit the curve.

The current implementation fixes N at 9 (so 9 x b(i) + 1 x kappa = 10
parameters). If the discount factor is constrained to be 1 at time t=0
(which is usually is) then one of the b(i)s is constrained, since at t=0,
sum(b(i)) = 1, reducing the total number of independent parameters to 9. In
the implementation b(1) is constrained.

 

>From my experience of using exponential spline fitting over the years, and
from what I have read, there is no definitive argument for fixing N=9.
Indeed the number chosen can depend on several considerations: the density
of bonds across the curve; whether you want to fit the very short end etc.
You also find that the value of kappa doesn't make much difference to the
quality of fit as long as it is in the right range. Other implementations
fix kappa (it's akin to the far-forward overnight rate, so something around
1% in the current environment), and then optimize over the b(i)s. If you
extrapolate the spline beyond the last bond (which is probably not a great
idea) then kappa does have an effect on the shape of that extrapolated part
but I feel it is simply an artefact of the fitting.

 

In my implementation, the number of parameters is a variable and hence a
class member, and there is also the option to fix kappa and supply a
non-zero value for that fix (kappa = 0 is a special case as it produces
df(t) = 1 no matter how much the b(i)s are varied (in the constrained model)
).

Initially I had derived my new class, unimaginatively named
ExponentialSplinesFittingN from ExponentialSplinesFitting, but on reflection
the inheritance is redundant as I am over-riding every method, so perhaps it
should also derive directly from the abstract base
FittedBondDiscountCurve::FittingMethod. I am open to suggestions for a
decent name!



I wrote it before I had read the QL "style guide" so will need to amend my
implantation anyway: hence this is a good moment to hear any thoughts!


Best wishes

David Sansom