[Quantlib-users] Forwards not matching nodes in monotone convex interpolation

[Tom A. <tw...@ur...>]

Hello,

If i build an interpolated forward curve, then i can get the nodes (date - 
rate pairs) of the interpolation out by doing:

curve->nodes()

and i can get instantaneous(-ish) forward rates out by doing:

curve->forwardRate(date, date, curve->dayCounter(), Compounding::Continuous).rate();

Should i in general expect that if i get the instantaneous forward rate on 
a date corresponding to a node, then it will equal the node's rate (modulo 
some small arithmetic errors)?

I would have naively throught i should. And looking at some 
interpolations, this seems to be the case.

But it seems not to be the case for monotone convex interpolation.

Monotone convex is just a piecewise quadratic spline under the hood, 
really; the complexity is in how the spline is constructed (although the 
original paper and the QuantLib implementation both somewhat obscure this 
fact). So i would have expected the nodes to behave like nodes of any 
other interpolation.

Is my expectation wrong? Or could this be a mistake in the implementation 
of monotone convex interpolation?

Thanks,
tom

-- 
Computation is the basis of all life