OvernightArithmeticCompoundingConvexity.java
package org.drip.sample.ois;
import java.util.*;
import org.drip.analytics.cashflow.CompositePeriod;
import org.drip.analytics.date.*;
import org.drip.analytics.support.*;
import org.drip.function.r1tor1.*;
import org.drip.market.otc.*;
import org.drip.numerical.common.FormatUtil;
import org.drip.param.creator.*;
import org.drip.param.market.*;
import org.drip.param.period.*;
import org.drip.param.valuation.*;
import org.drip.product.creator.*;
import org.drip.product.definition.CalibratableComponent;
import org.drip.product.rates.*;
import org.drip.service.env.EnvManager;
import org.drip.spline.basis.PolynomialFunctionSetParams;
import org.drip.spline.params.*;
import org.drip.spline.stretch.*;
import org.drip.state.creator.*;
import org.drip.state.discount.*;
import org.drip.state.estimator.LatentStateStretchBuilder;
import org.drip.state.identifier.*;
import org.drip.state.inference.*;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2018 Lakshmi Krishnamurthy
* Copyright (C) 2017 Lakshmi Krishnamurthy
* Copyright (C) 2016 Lakshmi Krishnamurthy
* Copyright (C) 2015 Lakshmi Krishnamurthy
* Copyright (C) 2014 Lakshmi Krishnamurthy
*
* This file is part of DRIP, a free-software/open-source library for buy/side financial/trading model
* libraries targeting analysts and developers
* https://lakshmidrip.github.io/DRIP/
*
* DRIP is composed of four main libraries:
*
* - DRIP Fixed Income - https://lakshmidrip.github.io/DRIP-Fixed-Income/
* - DRIP Asset Allocation - https://lakshmidrip.github.io/DRIP-Asset-Allocation/
* - DRIP Numerical Optimizer - https://lakshmidrip.github.io/DRIP-Numerical-Optimizer/
* - DRIP Statistical Learning - https://lakshmidrip.github.io/DRIP-Statistical-Learning/
*
* - DRIP Fixed Income: Library for Instrument/Trading Conventions, Treasury Futures/Options,
* Funding/Forward/Overnight Curves, Multi-Curve Construction/Valuation, Collateral Valuation and XVA
* Metric Generation, Calibration and Hedge Attributions, Statistical Curve Construction, Bond RV
* Metrics, Stochastic Evolution and Option Pricing, Interest Rate Dynamics and Option Pricing, LMM
* Extensions/Calibrations/Greeks, Algorithmic Differentiation, and Asset Backed Models and Analytics.
*
* - DRIP Asset Allocation: Library for model libraries for MPT framework, Black Litterman Strategy
* Incorporator, Holdings Constraint, and Transaction Costs.
*
* - DRIP Numerical Optimizer: Library for Numerical Optimization and Spline Functionality.
*
* - DRIP Statistical Learning: Library for Statistical Evaluation and Machine Learning.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
*
* You may obtain a copy of the License at
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
*
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/**
* OvernightArithmeticCompoundingConvexity contains an assessment of the impact of the Overnight Index
* Volatility, the Funding Numeraire Volatility, and the ON Index/Funding Correlation on the Overnight
* Floating Stream.
*
* @author Lakshmi Krishnamurthy
*/
public class OvernightArithmeticCompoundingConvexity {
private static final FixFloatComponent OTCOISFixFloat (
final JulianDate dtSpot,
final String strCurrency,
final String strMaturityTenor,
final double dblCoupon)
{
FixedFloatSwapConvention ffConv = OvernightFixedFloatContainer.FundConventionFromJurisdiction (
strCurrency
);
return ffConv.createFixFloatComponent (
dtSpot,
strMaturityTenor,
dblCoupon,
0.,
1.
);
}
/*
* Construct the Array of Deposit Instruments from the given set of parameters
*
* USE WITH CARE: This sample ignores errors and does not handle exceptions.
*/
private static final SingleStreamComponent[] DepositInstrumentsFromMaturityDays (
final JulianDate dtEffective,
final String strCurrency,
final int[] aiDay)
throws Exception
{
SingleStreamComponent[] aDeposit = new SingleStreamComponent[aiDay.length];
for (int i = 0; i < aiDay.length; ++i)
aDeposit[i] = SingleStreamComponentBuilder.Deposit (
dtEffective,
dtEffective.addBusDays (
aiDay[i],
strCurrency
),
OvernightLabel.Create (
strCurrency
)
);
return aDeposit;
}
private static final FixFloatComponent[] OISFromMaturityTenor (
final JulianDate dtSpot,
final String strCurrency,
final String[] astrMaturityTenor,
final double[] adblCoupon)
throws Exception
{
FixFloatComponent[] aOIS = new FixFloatComponent[astrMaturityTenor.length];
for (int i = 0; i < astrMaturityTenor.length; ++i)
aOIS[i] = OTCOISFixFloat (
dtSpot,
strCurrency,
astrMaturityTenor[i],
adblCoupon[i]
);
return aOIS;
}
private static final FixFloatComponent[] OISFuturesFromMaturityTenor (
final JulianDate dtSpot,
final String strCurrency,
final String[] astrStartTenor,
final String[] astrMaturityTenor,
final double[] adblCoupon)
throws Exception
{
FixFloatComponent[] aOISFutures = new FixFloatComponent[astrMaturityTenor.length];
for (int i = 0; i < astrMaturityTenor.length; ++i)
aOISFutures[i] = OTCOISFixFloat (
dtSpot.addTenor (astrStartTenor[i]),
strCurrency,
astrMaturityTenor[i],
adblCoupon[i]
);
return aOISFutures;
}
private static final MergedDiscountForwardCurve CustomOISCurveBuilderSample (
final JulianDate dtSpot,
final String strCurrency)
throws Exception
{
/*
* Construct the Array of Deposit Instruments and their Quotes from the given set of parameters
*/
SingleStreamComponent[] aDepositComp = DepositInstrumentsFromMaturityDays (
dtSpot,
strCurrency,
new int[] {
1, 2, 3
}
);
double[] adblDepositQuote = new double[] {
0.0004, 0.0004, 0.0004 // Deposit
};
/*
* Construct the Deposit Instrument Set Stretch Builder
*/
LatentStateStretchSpec depositStretch = LatentStateStretchBuilder.ForwardFundingStretchSpec (
" DEPOSIT ",
aDepositComp,
"ForwardRate",
adblDepositQuote
);
/*
* Construct the Array of Short End OIS Instruments and their Quotes from the given set of parameters
*/
double[] adblShortEndOISQuote = new double[] {
0.00070, // 1W
0.00069, // 2W
0.00078, // 3W
0.00074 // 1M
};
CalibratableComponent[] aShortEndOISComp = OISFromMaturityTenor (
dtSpot,
strCurrency,
new java.lang.String[] {
"1W", "2W", "3W", "1M"
},
adblShortEndOISQuote
);
/*
* Construct the Short End OIS Instrument Set Stretch Builder
*/
LatentStateStretchSpec oisShortEndStretch = LatentStateStretchBuilder.ForwardFundingStretchSpec (
"SHORT END OIS",
aShortEndOISComp,
"SwapRate",
adblShortEndOISQuote
);
/*
* Construct the Array of OIS Futures Instruments and their Quotes from the given set of parameters
*/
double[] adblOISFutureQuote = new double[] {
0.00046, // 1M x 1M
0.00016, // 2M x 1M
-0.00007, // 3M x 1M
-0.00013, // 4M x 1M
-0.00014 // 5M x 1M
};
CalibratableComponent[] aOISFutureComp = OISFuturesFromMaturityTenor (
dtSpot,
strCurrency,
new java.lang.String[] {
"1M", "2M", "3M", "4M", "5M"
},
new java.lang.String[] {
"1M", "1M", "1M", "1M", "1M"
},
adblOISFutureQuote
);
/*
* Construct the OIS Future Instrument Set Stretch Builder
*/
LatentStateStretchSpec oisFutureStretch = LatentStateStretchBuilder.ForwardFundingStretchSpec (
" OIS FUTURE ",
aOISFutureComp,
"SwapRate",
adblOISFutureQuote
);
/*
* Construct the Array of Long End OIS Instruments and their Quotes from the given set of parameters
*/
double[] adblLongEndOISQuote = new double[] {
0.00002, // 15M
0.00008, // 18M
0.00021, // 21M
0.00036, // 2Y
0.00127, // 3Y
0.00274, // 4Y
0.00456, // 5Y
0.00647, // 6Y
0.00827, // 7Y
0.00996, // 8Y
0.01147, // 9Y
0.01280, // 10Y
0.01404, // 11Y
0.01516, // 12Y
0.01764, // 15Y
0.01939, // 20Y
0.02003, // 25Y
0.02038 // 30Y
};
CalibratableComponent[] aLongEndOISComp = OISFromMaturityTenor (
dtSpot,
strCurrency,
new java.lang.String[] {
"15M", "18M", "21M", "2Y", "3Y", "4Y", "5Y", "6Y", "7Y", "8Y", "9Y", "10Y", "11Y", "12Y", "15Y", "20Y", "25Y", "30Y"
},
adblLongEndOISQuote
);
/*
* Construct the Long End OIS Instrument Set Stretch Builder
*/
LatentStateStretchSpec oisLongEndStretch = LatentStateStretchBuilder.ForwardFundingStretchSpec (
"LONG END OIS ",
aLongEndOISComp,
"SwapRate",
adblLongEndOISQuote
);
LatentStateStretchSpec[] aStretchSpec = new LatentStateStretchSpec[] {
depositStretch,
oisShortEndStretch,
oisFutureStretch,
oisLongEndStretch
};
/*
* Set up the Linear Curve Calibrator using the following parameters:
* - Cubic Exponential Mixture Basis Spline Set
* - Ck = 2, Segment Curvature Penalty = 2
* - Quadratic Rational Shape Controller
* - Natural Boundary Setting
*/
LinearLatentStateCalibrator lcc = new LinearLatentStateCalibrator (
new SegmentCustomBuilderControl (
MultiSegmentSequenceBuilder.BASIS_SPLINE_POLYNOMIAL,
new PolynomialFunctionSetParams (4),
SegmentInelasticDesignControl.Create (
2,
2
),
new ResponseScalingShapeControl (
true,
new QuadraticRationalShapeControl (0.)
),
null
),
BoundarySettings.NaturalStandard(),
MultiSegmentSequence.CALIBRATE,
null,
null
);
/*
* Construct the Shape Preserving Discount Curve by applying the linear curve calibrator to the array
* of Cash and Swap Stretches.
*/
return ScenarioDiscountCurveBuilder.ShapePreservingDFBuild (
strCurrency,
lcc,
aStretchSpec,
new ValuationParams (
dtSpot,
dtSpot,
strCurrency
),
null,
null,
null,
1.
);
}
private static final LatentStateFixingsContainer SetFlatOvernightFixings (
final JulianDate dtStart,
final JulianDate dtEnd,
final JulianDate dtValue,
final ForwardLabel fri,
final double dblFlatFixing,
final double dblNotional)
throws Exception
{
LatentStateFixingsContainer lsfc = new LatentStateFixingsContainer();
JulianDate dt = dtStart.addDays (1);
while (dt.julian() <= dtEnd.julian()) {
lsfc.add (
dt,
fri,
dblFlatFixing
);
dt = dt.addBusDays (1, "USD");
}
return lsfc;
}
private static final void SetMarketParams (
final int iValueDate,
final CurveSurfaceQuoteContainer mktParams,
final String strCurrency,
final ForwardLabel fri,
final double dblOISVol,
final double dblUSDFundingVol,
final double dblUSDFundingUSDOISCorrelation)
throws Exception
{
FundingLabel fundingLabel = FundingLabel.Standard (strCurrency);
mktParams.setForwardVolatility (
ScenarioDeterministicVolatilityBuilder.FlatForward (
iValueDate,
VolatilityLabel.Standard (fri),
fri.currency(),
dblOISVol
)
);
mktParams.setFundingVolatility (
ScenarioDeterministicVolatilityBuilder.FlatForward (
iValueDate,
VolatilityLabel.Standard (fundingLabel),
"USD",
dblUSDFundingVol
)
);
mktParams.setForwardFundingCorrelation (
fri,
fundingLabel,
new FlatUnivariate (dblUSDFundingUSDOISCorrelation)
);
}
private static final void VolCorrScenario (
final Stream[] aFloatStream,
final String strCurrency,
final ForwardLabel fri,
final ValuationParams valParams,
final CurveSurfaceQuoteContainer mktParams,
final double dblOISVol,
final double dblUSDFundingVol,
final double dblUSDFundingUSDOISCorrelation)
throws Exception
{
SetMarketParams (
valParams.valueDate(),
mktParams,
strCurrency,
fri,
dblOISVol,
dblUSDFundingVol,
dblUSDFundingUSDOISCorrelation
);
String strDump = "\t[" +
FormatUtil.FormatDouble (dblOISVol, 2, 0, 100.) + "%," +
FormatUtil.FormatDouble (dblUSDFundingVol, 2, 0, 100.) + "%," +
FormatUtil.FormatDouble (dblUSDFundingUSDOISCorrelation, 2, 0, 100.) + "%] = ";
for (int i = 0; i < aFloatStream.length; ++i) {
Map<String, Double> mapValue = aFloatStream[i].value (
valParams,
null,
mktParams,
null
);
if (0 != i) strDump += " || ";
strDump +=
FormatUtil.FormatDouble (mapValue.get ("UnadjustedFairPremium"), 1, 4, 100.) + "% | " +
FormatUtil.FormatDouble (mapValue.get ("CompoundingAdjustmentFactor") - 1, 1, 2, 100.) + "% | " +
FormatUtil.FormatDouble (mapValue.get ("CumulativeConvexityAdjustmentFactor") - 1, 1, 2, 100.) + "%";
}
System.out.println (strDump);
}
public static final void main (
final String[] astrArgs)
throws Exception
{
/*
* Initialize the Credit Analytics Library
*/
EnvManager.InitEnv ("");
JulianDate dtToday = DateUtil.Today().addTenor ("0D");
String strCurrency = "USD";
MergedDiscountForwardCurve dc = CustomOISCurveBuilderSample (
dtToday,
strCurrency
);
JulianDate dtCustomOISStart = dtToday.subtractTenor ("2M");
JulianDate dtCustomOISMaturity = dtToday.addTenor ("4M");
ForwardLabel fri = OvernightLabel.Create (strCurrency);
ComposableFloatingUnitSetting cfusFloating = new ComposableFloatingUnitSetting (
"ON",
CompositePeriodBuilder.EDGE_DATE_SEQUENCE_OVERNIGHT,
null,
OvernightLabel.Create (
strCurrency
),
CompositePeriodBuilder.REFERENCE_PERIOD_IN_ADVANCE,
0.
);
CompositePeriodSetting cpsFloating = new CompositePeriodSetting (
360,
"ON",
strCurrency,
null,
-1.,
null,
null,
null,
null
);
List<Integer> lsFloatingStreamEdgeDate = CompositePeriodBuilder.RegularEdgeDates (
dtCustomOISStart,
"6M",
"6M",
null
);
List<CompositePeriod> lsCP = CompositePeriodBuilder.FloatingCompositeUnit (
lsFloatingStreamEdgeDate,
cpsFloating,
cfusFloating
);
Stream floatStream = new Stream (lsCP);
CurveSurfaceQuoteContainer mktParams = MarketParamsBuilder.Create (
dc,
null,
null,
null,
null,
null,
SetFlatOvernightFixings (
dtCustomOISStart,
dtCustomOISMaturity,
dtToday,
fri,
0.003,
-1.
)
);
ValuationParams valParams = new ValuationParams (
dtToday,
dtToday,
strCurrency
);
double[] adblOISVol = new double [] {
0.1, 0.3, 0.5
};
double[] adblUSDFundingVol = new double [] {
0.1, 0.3, 0.5
};
double[] adblUSDFundingUSDOISCorrelation = new double [] {
-0.3, 0.0, 0.3
};
System.out.println ("\n\t-------------------------------------------------------------------------------------");
System.out.println ("\tInput Order (LHS) L->R:");
System.out.println ("\t\tOIS Volatility, Funding Volatility, OIS/Funding Correlation\n");
System.out.println ("\tOutput Order (RHS) L->R:");
System.out.println ("\t\tUnadjusted Fair Premium, Compounding Adjustment Factor (% - Relative), Convexity Adjustment Factor (% - Relative)\n");
System.out.println ("\t-------------------------------------------------------------------------------------");
for (double dblOISVol : adblOISVol) {
for (double dblUSDFundingVol : adblUSDFundingVol) {
for (double dblUSDFundingUSDOISCorrelation : adblUSDFundingUSDOISCorrelation)
VolCorrScenario (
new Stream[] {floatStream},
strCurrency,
fri,
valParams,
mktParams,
dblOISVol,
dblUSDFundingVol,
dblUSDFundingUSDOISCorrelation
);
}
}
System.out.println ("\t-------------------------------------------------------------------------------------");
}
}