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

[Luigi B. <lui...@gm...>]

Hi, not much is already existing, I'm afraid.  You can have a look at
Goutham's post at
https://gouthamanbalaraman.com/blog/hull-white-simulation-quantlib-python.html
(also in the cookbook if you have it) for a few ideas; he generates
interest-rate paths based on a Hull/White model, but something similar
should work for G2 as well.

Hope this helps,
    Luigi


On Wed, Jan 24, 2024 at 8:03 PM Philippe Hatstadt <
phi...@ex...> wrote:

> 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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