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

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No, I'm afraid G2 is the only two-factor model we have in that framework.
There's also an implementation of LMM from the late Mark Joshi, but I'm not
familiar with it.

Luigi

On Tue, Feb 6, 2024 at 1:29 PM Philippe Hatstadt <
phi...@ex...> wrote:

> Thanks Luigi. Wow 18 years…
> Are there other models that can de-correlate CMS2Y versus CMS10Y and
> longer? Working in OAS model where slope of the curve is a principal
> component.
> Regards
>
> Philippe Hatstadt
> +1-203-252-0408
>
>
> On Feb 6, 2024, at 7:00 AM, Luigi Ballabio <lui...@gm...>
> wrote:
>
> 
> Hmm—you're right, it looks like the G2 processes are only half-done.  From
> the git logs of the C++ library, it looks like they were added 18 years ago
> and never updated (and probably never used either).  They should be fixed
> there.  I've opened https://github.com/lballabio/QuantLib/issues/1904 but
> I don't know when someone will pick it up.
>
> 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
>>>>>>
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