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

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@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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>>
>> 1370 Broadway, Suite 1450 | New York, NY | 10018
>>
>> [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>.
>>
>>
>> Confidentiality Notice: The information contained in this email
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>

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