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

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Hi Philippe,
     there's now a pull request (
https://github.com/lballabio/QuantLib/pull/1937) that aims at fixing the G2
process including the term structure.  May you check if the changes make
sense to you?  Thanks!

Luigi


On Mon, Feb 5, 2024 at 8:44 PM Philippe Hatstadt <
phi...@ex...> wrote:

> @Luigi Ballabio <lui...@gm...> trying to follow up on this
> discussion. Here is what I found at the Python level.
>
> A. Apparently, there is a well-defined way of generating short rate paths
> for HW1F as follows, per cookbook, and post calibration of a and sigma:
>
> hw_process = HullWhiteProcess(spot_curve_handle, a, sigma)
> rng = GaussianRandomSequenceGenerator(
>     UniformRandomSequenceGenerator(timestep, UniformRandomGenerator()))
> seq = GaussianPathGenerator(hw_process, length, timestep, rng, False)
>
> B. For G2 model, I was able to find this: g2pp_fprocess =
> G2ForwardProcess(a, sigma, b, eta, rho) or g2pp_process = G2Process(a,
> sigma, b, eta, rho). What is puzzling is that neither call takes
> spot_curve_handle as a parameter, which is confirmed by the SWIG
> extract below. Does it mean that either of G2Process() / G2ForwardProcess()
> classes are not "finished" products, and/or am I supposed to pass the term
> structure handle in a different way? More generally, how am I supposed to
> use this class, if at all?
>
> # Register G2Process in _QuantLib:
> _QuantLib.G2Process_swigregister(G2Process)
> class G2ForwardProcess(StochasticProcess):
>     r"""Proxy of C++ G2ForwardProcess class."""
>
>     thisown = property(lambda x: x.this.own(), lambda x, v: x.this.own(v), doc="The membership flag")
>     __repr__ = _swig_repr
>
>
>     def __init__(self, a, sigma, b, eta, rho):
>         r"""__init__(G2ForwardProcess self, Real a, Real sigma, Real b, Real eta, Real rho) -> G2ForwardProcess"""
>         _QuantLib.G2ForwardProcess_swiginit(self, _QuantLib.new_G2ForwardProcess(a, sigma, b, eta, rho))
>
>
> Philippe Hatstadt
>
>
> On Tue, Jan 30, 2024 at 11:29 AM philippe hatstadt <pha...@ma...>
> wrote:
>
>> Yeah that’s what I was thinking. At least I’d be making indirect C++
>> calls. I might try.
>> Regards
>>
>> Philippe Hatstadt
>> +1-203-252-0408
>>
>>
>> On Jan 30, 2024, at 11:15 AM, Luigi Ballabio <lui...@gm...>
>> wrote:
>>
>> 
>> Hmm, I'm not sure.   The only thing that comes to mind is that, given a
>> path for interest rates, one could create some sort of interest-rate term
>> structure and then extract CMT rates from it.  It's not something I tried,
>> though.
>>
>> Luigi
>>
>> On Tue, Jan 30, 2024 at 1:39 PM Philippe Hatstadt <
>> phi...@ex...> wrote:
>>
>>> Except I need to generate CMT rates along each path for my prepayment
>>> model. That would have be to be a pure  Python Ioop? How would you then
>>> advise to calculate CMT rates from a path of short rates with the goal to
>>> try and use as many wrapped Python calls to underlying C++?
>>>
>>> Regards
>>>
>>> Philippe Hatstadt
>>> +1-203-252-0408
>>>
>>>
>>> On Jan 30, 2024, at 7:33 AM, Luigi Ballabio <lui...@gm...>
>>> wrote:
>>>
>>> 
>>> It might not be so bad.  The generation of the paths is driven from
>>> Python but performed by the GaussianPathGenerator class in C++.  I'd
>>> give it a try.
>>>
>>> Luigi
>>>
>>>
>>> On Tue, Jan 30, 2024 at 1:28 PM Philippe Hatstadt <
>>> phi...@ex...> wrote:
>>>
>>>> Thank you. I looked at it and it’s great. His post-calibration
>>>>  simulation on HW is done in Python though so performance will be an issue.
>>>> Thence my asking if there were routines existing in C++.
>>>>
>>>> Thank you.
>>>>
>>>> Regards
>>>>
>>>> Philippe Hatstadt
>>>> +1-203-252-0408
>>>>
>>>>
>>>> On Jan 30, 2024, at 7:24 AM, Luigi Ballabio <lui...@gm...>
>>>> wrote:
>>>>
>>>> 
>>>> 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
>>>>>
>>>>> 1370 Broadway, Suite 1450 | New York, NY | 10018
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