[Quantlib-users] Forward CMT rates from G2++ calibrated model for OAS model

[Philippe H. <phi...@ex...>]

I was able to calibrate a G2++ model to normal UST swaption volatilities
(heroically using SOFR swaptions and re-scaling by rates ratio to generate
so-called Treasury Swaption vol surface).
Code is below:

model = G2(term_structure);
# engine = TreeSwaptionEngine(model, 25)
# engine = ql.G2SwaptionEngine(model, 10, 400)
engine = ql.FdG2SwaptionEngine(model)
swaptions = create_swaption_helpers_normal(data, index, term_structure,
engine)
optimization_method = LevenbergMarquardt(1.0e-8,1.0e-8,1.0e-8)
end_criteria = EndCriteria(1000, 100, 1e-6, 1e-8, 1e-8)
model.calibrate(swaptions, optimization_method, end_criteria)
a, sigma, b, eta, rho = model.params()\

The question now is as follows: I want to use this model towards a GNMA OAS
model for which I would need monte-carlo paths of 2y/5y/10y forward CMT
rates spaced say monthly.

I assume that I would first need to use the 5 G2++ parameters calibrated
above and then generate paths of the short rate, then somehow compute
forward CMT at each forward monthly epoch Ti by computing the break-even
coupon C10(Ti) such that PV(Ti, bond(cpn=C10(Ti)) == 100?
Are there existing QL classes or modules that do all that from a given
calibrated model like above?
By the same token, I would also need stochastic pathwise discount factor
vectors DF(Ti, path j), i=0 to 30y monthly. Is there also a QL module that
generates those? I can obviously do it manually, but I am on the python
side, so I want to re-use as much of existing libraries as I can to use
efficient C++ code indirectly via SWIG.

Regards

Philippe Hatstadt

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