Hi, the zeroRate() function (applied to YieldTermStructure object) appears to be returning zero rates that are too large. To illustrate, I constructed a simple example based largely on code snippets from /testsuite/piecewiseyieldcurve.cpp.
In brief:
* Input a flat term structure of deposit + swap rates of 5.0% out to 30 years.
Datum depositData[] = { { 1, Weeks, 5.0 }};
Datum swapData[] = {
{ 1, Years, 5.0 }, { 2, Years, 5.0 }, { 3, Years, 5.0 },
.... { 30, Years, 5.0 } };
* Very minor changes to settings in CommonVars, to construction of "rates" and "instruments" vectors [adpated to USDLibor rather than Euribor---conclusions are unaffected by that switch].
-> all the info from this stage goes into "vars".
* PiecewiseYieldCurve set up as follows:
template <class T, class I, template<class C> class B>
CommonVars CurveMake(CommonVars& vars,
const I& interpolator = I(), Real tolerance = 1.0e-9) {
vars.termStructure = boost::shared_ptr<YieldTermStructure>(new
PiecewiseYieldCurve<T,I,B>(vars.settlement, vars.instruments,
Actual360(), interpolator));
...etc....
* Called CurveMake as follows (from main):
CommonVars varsOut =
CurveMake<ZeroYield,Linear,IterativeBootstrap>(vars);
* Retrieve curve info via:
boost::shared_ptr<YieldTermStructure> yc= varsOut.termStructure;
* For output, set up vector of target dates (rTdates), and called zeroRate() and discount(); & computed implied zero from discount() as follows:
d0=varsOut.settlement;
for (Size i=0; i<rtDates.size(); i++) {
Real rx, df; dx=rtDates[i];
rx = Rate(yc->zeroRate(dx,dc, Simple, Annual, true));
df = yc->discount(dx, true);
Real zeroFromDf= -log(df)/((dx-d0)/365.);
wtfil2 << std::setw(7) <<std::setprecision(2) << (dx-d0)/365.
<< std::setw(10) << std::setprecision(4) << rx
<<std::setw(10) << std::setprecision(6) << df
<< std::setw(10) << std::setprecision(4) << zeroFromDf
<<std::endl;
}
* OUTPUT:
[DayCounter= Actual/Actual (ISDA]
Implied
Zero rate from
t (Yrs) zeroRate() discount() discount()
0.5 0.0507 0.975209 0.05007
1 0.05069 0.951751 0.04945
2 0.052 0.905711 0.04945
5 0.05614 0.780837 0.04945
10 0.06402 0.609626 0.04945
20 0.08447 0.371827 0.04943
30 0.1138 0.226552 0.04946
35 0.1331 0.176776 0.04948
********************************************
So, the implied zero from discount() is close to (but not dead on) the expected 5.0%, but the zeroRate() seems to drift away considerably. Similar patterns are observed after toggling various settings and parameters (e.g., DayCounters,
call CurveMake with Discount instead of ZeroYield, etc.)
Am I doing something wrong or misunderstanding what zeroRate() is supposed to be returning?
Any help appreciated. Thanks
P.C. Venkatesh
Stress Testing
Division of Banking Supervision & Regulation
Board of Governors of the Federal Reserve System
vox: 202 452 3847
email: [hidden email]
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