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

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<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body dir="auto">Thanks Luigi. Wow 18 years…&nbsp;<div>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.<br id="lineBreakAtBeginningOfSignature"><div dir="ltr">Regards<div><br></div><div>Philippe Hatstadt</div><div>+1-203-252-0408</div><div><br></div></div><div dir="ltr"><br><blockquote type="cite">On Feb 6, 2024, at 7:00 AM, Luigi Ballabio &lt;lui...@gm...&gt; wrote:<br><br></blockquote></div><blockquote type="cite"><div dir="ltr"><div dir="ltr">Hmm—you're right, it looks like the G2 processes are only half-done.&nbsp; 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).&nbsp; They should be fixed there.&nbsp; I've opened&nbsp;<a href="https://github.com/lballabio/QuantLib/issues/1904">https://github.com/lballabio/QuantLib/issues/1904</a> but I don't know when someone will pick it up.<div><br></div><div>Luigi</div><div><br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Mon, Feb 5, 2024 at 8:44 PM Philippe Hatstadt &lt;<a href="mailto:phi...@ex...">phi...@ex...</a>&gt; wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><a class="gmail_plusreply" id="m_5661415589927083342plusReplyChip-0" href="mailto:lui...@gm..." target="_blank">@Luigi Ballabio</a>&nbsp;trying to follow up on this discussion. Here is what I found at the Python level.<div><br></div><div>A. Apparently, there is a well-defined way of generating short rate paths for HW1F as follows, per cookbook, and post calibration&nbsp;of a and sigma:<div><br><div>hw_process = HullWhiteProcess(spot_curve_handle, a, sigma)<br>rng = GaussianRandomSequenceGenerator(<br>&nbsp; &nbsp; UniformRandomSequenceGenerator(timestep, UniformRandomGenerator()))<br>seq = GaussianPathGenerator(hw_process, length, timestep, rng, False)</div><div><br></div><div>B. For G2 model, I was able to find this:&nbsp;g2pp_fprocess = G2ForwardProcess(a, sigma, b, eta, rho) or&nbsp;g2pp_process = G2Process(a, sigma, b, eta, rho). What is puzzling is that neither call takes spot_curve_handle as a parameter, which&nbsp;is confirmed by the SWIG extract&nbsp;below. Does it mean that either of G2Process() / G2ForwardProcess() classes are not "finished" products, and/or am I supposed&nbsp;to pass the term structure handle in a different way? More generally, how am I&nbsp;supposed to use this class, if at all?&nbsp;&nbsp;</div><div><span style="color:rgb(0,0,0)"><br></span></div><div><span style="color:rgb(0,0,0)"># Register G2Process in _QuantLib:</span></div><div><span style="font-family:arial,sans-serif;color:rgb(0,0,0)">_QuantLib.G2Process_swigregister(G2Process)</span></div><div><span style="font-family:arial,sans-serif;color:rgb(0,0,0)">class G2ForwardProcess(StochasticProcess):</span></div><div><span style="font-family:arial,sans-serif;color:rgb(0,0,0)">&nbsp; &nbsp; r"""Proxy of C++ G2ForwardProcess class."""</span></div><div><pre style="color:rgb(0,0,0)"><font face="arial, sans-serif">    thisown = property(lambda x: x.this.own(), lambda x, v: x.this.own(v), doc="The membership flag")
    __repr__ = _swig_repr</font></pre><pre style="color:rgb(0,0,0)"><font face="arial, sans-serif">
    def __init__(self, a, sigma, b, eta, rho):
        r"""__init__(G2ForwardProcess self, Real a, Real sigma, Real b, Real eta, Real rho) -&gt; G2ForwardProcess"""
        _QuantLib.G2ForwardProcess_swiginit(self, _QuantLib.new_G2ForwardProcess(a, sigma, b, eta, rho))</font></pre></div><div><br clear="all"><div><div dir="ltr" class="gmail_signature"><div dir="ltr">Philippe Hatstadt</div></div></div><br></div></div></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Tue, Jan 30, 2024 at 11:29 AM philippe hatstadt &lt;<a href="mailto:pha...@ma..." target="_blank">pha...@ma...</a>&gt; wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="auto">Yeah that’s what I was thinking. At least I’d be making indirect C++ calls. I might try.<br id="m_5661415589927083342m_-6559702879327117141lineBreakAtBeginningOfSignature"><div dir="ltr">Regards<div><br></div><div>Philippe Hatstadt</div><div>+1-203-252-0408</div><div><br></div></div><div dir="ltr"><br><blockquote type="cite">On Jan 30, 2024, at 11:15 AM, Luigi Ballabio &lt;<a href="mailto:lui...@gm..." target="_blank">lui...@gm...</a>&gt; wrote:<br><br></blockquote></div><blockquote type="cite"><div dir="ltr"><div dir="ltr">Hmm, I'm not sure.&nbsp; &nbsp;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.&nbsp; It's not something I tried, though.<div><br></div><div>Luigi</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Tue, Jan 30, 2024 at 1:39 PM Philippe Hatstadt &lt;<a href="mailto:phi...@ex..." target="_blank">phi...@ex...</a>&gt; wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="auto">Except I need to generate CMT rates along each path for my prepayment model. That would have be to be a pure &nbsp;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++?<div><br id="m_5661415589927083342m_-6559702879327117141m_-5301017114382669129lineBreakAtBeginningOfSignature"><div dir="ltr">Regards<div><br></div><div>Philippe Hatstadt</div><div>+1-203-252-0408</div><div><br></div></div><div dir="ltr"><br><blockquote type="cite">On Jan 30, 2024, at 7:33 AM, Luigi Ballabio &lt;<a href="mailto:lui...@gm..." target="_blank">lui...@gm...</a>&gt; wrote:<br><br></blockquote></div><blockquote type="cite"><div dir="ltr"><div dir="ltr">It might not be so bad.&nbsp; The generation of the paths is driven from Python but performed by the&nbsp;<span style="color:rgb(0,0,0)">GaussianPathGenerator class in C++.&nbsp; I'd give it a try.</span><div><span style="color:rgb(0,0,0)"><br></span></div><div><span style="color:rgb(0,0,0)">Luigi</span></div><div><span style="color:rgb(0,0,0)"><br></span></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Tue, Jan 30, 2024 at 1:28 PM Philippe Hatstadt &lt;<a href="mailto:phi...@ex..." target="_blank">phi...@ex...</a>&gt; wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="auto">Thank you. I looked at it and it’s great. His post-calibration &nbsp;simulation on HW is done in Python though so performance will be an issue. Thence my asking if there were routines existing in C++.<div><br><div>Thank you.<br><div><br id="m_5661415589927083342m_-6559702879327117141m_-5301017114382669129m_-1044749212735144493lineBreakAtBeginningOfSignature"><div dir="ltr">Regards<div><br></div><div>Philippe Hatstadt</div><div>+1-203-252-0408</div><div><br></div></div><div dir="ltr"><br><blockquote type="cite">On Jan 30, 2024, at 7:24 AM, Luigi Ballabio &lt;<a href="mailto:lui...@gm..." target="_blank">lui...@gm...</a>&gt; wrote:<br><br></blockquote></div><blockquote type="cite"><div dir="ltr"><div dir="ltr">Hi, not much&nbsp;is already existing, I'm afraid.&nbsp; You can have a look at Goutham's post at&nbsp;<a href="https://gouthamanbalaraman.com/blog/hull-white-simulation-quantlib-python.html" target="_blank">https://gouthamanbalaraman.com/blog/hull-white-simulation-quantlib-python.html</a> (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.<div><br></div><div>Hope this helps,</div><div>&nbsp; &nbsp; Luigi</div><div><br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Wed, Jan 24, 2024 at 8:03 PM Philippe Hatstadt &lt;<a href="mailto:phi...@ex..." target="_blank">phi...@ex...</a>&gt; wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div>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).</div><div>Code is below:</div><div><br></div><div>model = G2(term_structure);<br># engine = TreeSwaptionEngine(model, 25)<br># engine = ql.G2SwaptionEngine(model, 10, 400)<br>engine = ql.FdG2SwaptionEngine(model)<br>swaptions = create_swaption_helpers_normal(data, index, term_structure, engine)<br>optimization_method = LevenbergMarquardt(1.0e-8,1.0e-8,1.0e-8)<br>end_criteria = EndCriteria(1000, 100, 1e-6, 1e-8, 1e-8)<br>model.calibrate(swaptions, optimization_method, end_criteria)<br></div><div>a, sigma, b, eta, rho = model.params()\<br></div><div><br></div><div>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.</div><div><br></div><div>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&nbsp;forward monthly epoch Ti by computing the break-even coupon C10(Ti) such that PV(Ti, bond(cpn=C10(Ti)) == 100?</div><div>Are there existing QL classes or modules that do all that from a given calibrated model like above?</div><div>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&nbsp;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&nbsp;C++ code indirectly via SWIG.</div><div><br></div><div>Regards&nbsp;</div><br clear="all"><div><div dir="ltr" class="gmail_signature"><div dir="ltr">Philippe Hatstadt</div></div></div></div>

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