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

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If you are willing to use the ORE libraries (extension to QuantLib), there
is a nF-Hull-White Model. It is work in progress, calibration to options
and time-dependent parameters are still missing. It's particularly suitable
to reproduce movements taken from a PCA on historical curve data. Here are
links to some demos:

https://github.com/OpenSourceRisk/Engine/tree/master/Examples/Example_37
https://github.com/OpenSourceRisk/Engine/tree/master/Examples/Example_38

Best
Peter

On Tue, 6 Feb 2024 at 17:01, Luigi Ballabio <lui...@gm...>
wrote:

> 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
>>>>>>>
>>>>>>> 1370 Broadway, Suite 1450 | New York, NY | 10018
>>>>>>>
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>>>>>>> <https://www.exosfinancial.com/> [image:
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>>>>>>
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>>>>>> <https://www.exosfinancial.com/> [image:
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>>>>>
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>>>>>
>>>>> [image: https://www.exosfinancial.com/]
>>>>> <https://www.exosfinancial.com/> [image:
>>>>> https://www.linkedin.com/company/meetexos/about/]
>>>>> <https://www.linkedin.com/company/meetexos/about/>
>>>>>
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>>>>> SIPC, FINRA. For important disclosures including Form CRS and Regulation BI
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>>>>>
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>>
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>>
>> [image: https://www.exosfinancial.com/] <https://www.exosfinancial.com/> [image:
>> https://www.linkedin.com/company/meetexos/about/]
>> <https://www.linkedin.com/company/meetexos/about/>
>>
>> Broker-Dealer services offered through Exos Securities LLC, Member SIPC,
>> FINRA. For important disclosures including Form CRS and Regulation BI click
>> here <https://www.exosfinancial.com/general-disclosures>.
>>
>>
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