Interpretation of scenariodump.csv

[Anonymous]

Dear All!

I’m trying to understand the Output of scenariodump.csv (readable Scenario marketdata) and I believe that there is some additional tweaking necessary.
The Discount Curves (DiscountCurve/CAD/0, DiscountCurve/CAD/1, ….) are in my assumption all discount factors at the given Tenor (0=3M,1=6M,…11=20Y in my case):
` <YieldCurves>
<Configuration>
<Tenors>3M,6M,1Y,2Y,3Y,4Y,5Y,7Y,10Y,12Y,15Y,20Y</Tenors>
<Interpolation>LogLinear</Interpolation>
<Extrapolation>Y</Extrapolation>
</Configuration>
</YieldCurves>

Now, the maximum “discount factor” for the 20Y-CAD Tenor over all Scenarios is 3.36, which would imply a zero-rate of ~ -5.8% (roughly calculated with (1/DF)^(1/T)-1 ), which seems pretty improbable to me.
The same applies to CHF, GBP, and – not so extreme – to EUR, USD and JPY (but even a negative rate of -2.4% seems strange for a 20Y Tenor in JPY).

The Indices (IndexCurve/EUR-EURIBOR-3M/0 …) are similarly strange to Interpret, they look also like discount factors to me…

Is there some additional calculation with the given numeraire column to be done?

-regards,
Roland

[Anonymous]

Maybe I should add that all foreign currency (non EUR) curves are set up as “collateral in EUR” curves, i.e. the foreign Ccy cashflows are discounted using the EUR1D (EONIA Swap) curve + the Basis swap spread:

` <YieldCurve>
<CurveId>CHF-IN-EUR</CurveId>
<CurveDescription>CHF collateralized in EUR discount curve</CurveDescription>
<Currency>CHF</Currency>
<DiscountCurve/>
<Segments>
<CrossCurrency>
<Type>Cross Currency Basis Swap</Type>
<Quotes>
<Quote>CC_BASIS_SWAP/BASIS_SPREAD/EUR/3M/CHF/3M/1Y</Quote>
<Quote>CC_BASIS_SWAP/BASIS_SPREAD/EUR/3M/CHF/3M/2Y</Quote>
<Quote>CC_BASIS_SWAP/BASIS_SPREAD/EUR/3M/CHF/3M/3Y</Quote>
<Quote>CC_BASIS_SWAP/BASIS_SPREAD/EUR/3M/CHF/3M/4Y</Quote>
<Quote>CC_BASIS_SWAP/BASIS_SPREAD/EUR/3M/CHF/3M/5Y</Quote>
<Quote>CC_BASIS_SWAP/BASIS_SPREAD/EUR/3M/CHF/3M/7Y</Quote>
<Quote>CC_BASIS_SWAP/BASIS_SPREAD/EUR/3M/CHF/3M/10Y</Quote>
<Quote>CC_BASIS_SWAP/BASIS_SPREAD/EUR/3M/CHF/3M/15Y</Quote>
<Quote>CC_BASIS_SWAP/BASIS_SPREAD/EUR/3M/CHF/3M/20Y</Quote>
</Quotes>
<Conventions>EUR-CHF-XCCY-BASIS-CONVENTIONS</Conventions>
<DiscountCurve>EUR1D</DiscountCurve>
<SpotRate>FX/RATE/EUR/CHF</SpotRate>
<ProjectionCurveDomestic>CHF3M</ProjectionCurveDomestic>
<ProjectionCurveForeign>EUR3M</ProjectionCurveForeign>
</CrossCurrency>
</Segments>
<InterpolationVariable>Discount</InterpolationVariable>
<InterpolationMethod>LogLinear</InterpolationMethod>
<YieldCurveDayCounter>A365</YieldCurveDayCounter>
<Tolerance>0.000000000001</Tolerance>
</YieldCurve>

Could it be that this leads to These strange simulation results?

-regards,
Roland

[Anonymous]

OK, I’ve seen from the test cases that indeed there is a need to divide all scenario data by the numeraire:
…
` // Basic martingale tests
Size samples = 10000;
Real eur = 0.0, usd = 0.0, gbp = 0.0, eur2 = 0.0, usd2 = 0.0, gbp2 = 0.0;

boost::timer timer;
for (Size i = 0; i < samples; i++) {
for (Date d : grid->dates()) {
boost::shared_ptr<Scenario> scenario = scenGen->next(d);

if (d == grid->dates().back()) { // in 10 years from today
RiskFactorKey eurKey(RiskFactorKey::KeyType::DiscountCurve, “EUR”, 8);
RiskFactorKey usdKey(RiskFactorKey::KeyType::DiscountCurve, “USD”, 8);
RiskFactorKey gbpKey(RiskFactorKey::KeyType::DiscountCurve, “GBP”, 8);
RiskFactorKey usdeurKey(RiskFactorKey::KeyType::FXSpot, “USDEUR”);
RiskFactorKey gbpeurKey(RiskFactorKey::KeyType::FXSpot, “GBPEUR”);

Real usdeurFX = scenario->get(usdeurKey);
Real gbpeurFX = scenario->get(gbpeurKey);
Real numeraire = scenario->getNumeraire();
Real eur10yDiscount = scenario->get(eurKey);
Real gbp10yDiscount = scenario->get(gbpKey);
Real usd10yDiscount = scenario->get(usdKey);
eur += eur10yDiscount / numeraire;
gbp += gbp10yDiscount * gbpeurFX / numeraire;
usd += usd10yDiscount * usdeurFX / numeraire;
eur2 += 1.0 / numeraire;
gbp2 += gbpeurFX / numeraire;
usd2 += usdeurFX / numeraire;
}
}
}
Real elapsed = timer.elapsed();

eur /= samples;
gbp /= samples;
usd /= samples;
eur2 /= samples;
gbp2 /= samples;
usd2 /= samples;

Real relTolerance = 0.01;
Real eurExpected = d.market->discountCurve(“EUR”)->discount(20.);
BOOST_CHECK_MESSAGE(fabs(eur – eurExpected) / eurExpected < relTolerance,
“EUR 20Y Discount mismatch: ” << eur << ” vs ” << eurExpected);

…

Doing this results in a “shock” inverse scenario with very low discount factors at the short end (giving a ~60000% zero rate) and moderately low rates at the long end (~2% zero rate) … well, it’s the highest CAD discount rate in all scenarios …

Furthermore, I’ve seen that the index curve needs to be interpreted as discount factors, also needing above correction with the numeraire.

-regards,
Roland

[Roland Lichters]

Hi Roland,

apologies for the delay, but you have answered it already.

I just want to point you to a configuration option that introduces a change of measure and therefore affects the scenario dump output. Example section 4.13 in the ORE user guide illustrates it- parameter “ShiftHorizon” in the simulation model configuration (when set to a time larger than 0) changes measure from the LGM measure to the Hull-White T-Forward measure which has quite a significant effect in long-term simulations, see figure 20.

Regards,
Roland

[Author]

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