LIBORMarketModelStandard.java

/*
 * (c) Copyright Christian P. Fries, Germany. All rights reserved. Contact: email@christian-fries.de.
 *
 * Created on 09.02.2004
 */
package net.finmath.montecarlo.interestrate;

import java.util.ArrayList;
import java.util.Map;

import net.finmath.exception.CalculationException;
import net.finmath.functions.AnalyticFormulas;
import net.finmath.marketdata.model.AnalyticModelInterface;
import net.finmath.marketdata.model.curves.DiscountCurveFromForwardCurve;
import net.finmath.marketdata.model.curves.DiscountCurveInterface;
import net.finmath.marketdata.model.curves.ForwardCurveInterface;
import net.finmath.marketdata.model.volatilities.AbstractSwaptionMarketData;
import net.finmath.marketdata.products.Swap;
import net.finmath.marketdata.products.SwapAnnuity;
import net.finmath.montecarlo.RandomVariable;
import net.finmath.montecarlo.interestrate.modelplugins.AbstractLIBORCovarianceModel;
import net.finmath.montecarlo.interestrate.modelplugins.AbstractLIBORCovarianceModelParametric;
import net.finmath.montecarlo.interestrate.products.AbstractLIBORMonteCarloProduct;
import net.finmath.montecarlo.interestrate.products.SwaptionAnalyticApproximation;
import net.finmath.montecarlo.interestrate.products.SwaptionSimple;
import net.finmath.montecarlo.model.AbstractModel;
import net.finmath.stochastic.RandomVariableInterface;
import net.finmath.time.RegularSchedule;
import net.finmath.time.ScheduleInterface;
import net.finmath.time.TimeDiscretization;
import net.finmath.time.TimeDiscretizationInterface;

/**
 * Implements a basic LIBOR market model with some drift approximation methods.
 * <br>
 * The class implements different measure(drift) / numeraire pairs (terminal and spot).
 * <br>
 * The class specifies a LIBOR market model in its log-normal formulation, that is
 * <i>L<sub>j</sub> = exp(Y<sub>j</sub>) </i> where
 * <br>
 * <i>dY<sub>j</sub> = μ<sub>j</sub> dt + λ<sub>1,j</sub> dW<sub>1</sub> + ... + λ<sub>m,j</sub> dW<sub>m</sub></i>
 * <br>
 * see {@link net.finmath.montecarlo.model.AbstractModelInterface} for details on the implemented interface.
 * <br>
 * The model uses an <code>AbstractLIBORCovarianceModel</code> for the specification of <i>(λ<sub>1,j</sub>,...,λ<sub>m,j</sub>)</i> as a covariance model,
 * which may have the ability to calibrate to swaptions.
 * 
 * @see net.finmath.montecarlo.interestrate.modelplugins.AbstractLIBORCovarianceModel
 * 
 * @author Christian Fries
 * @version 1.1
 */
public class LIBORMarketModelStandard extends AbstractModel implements LIBORMarketModelInterface {

	private static final boolean isUseAnalyticApproximation;
	static {
		// Default value is true;
		isUseAnalyticApproximation = Boolean.parseBoolean(System.getProperty("net.finmath.montecarlo.interestrate.LIBORMarketModelStandard.isUseAnalyticApproximation","true"));
	}

	public enum Driftapproximation	{ EULER, LINE_INTEGRAL, PREDICTOR_CORRECTOR }

	public enum Measure				{ SPOT, TERMINAL }

	private final TimeDiscretizationInterface		liborPeriodDiscretization;

	private String							forwardCurveName;
	private AnalyticModelInterface			curveModel;

	private ForwardCurveInterface			forwardRateCurve;
	private DiscountCurveInterface			discountCurve;

	private AbstractLIBORCovarianceModel	covarianceModel;

	private AbstractSwaptionMarketData		swaptionMarketData;

	private Driftapproximation	driftApproximationMethod	= Driftapproximation.EULER;
	private Measure				measure						= Measure.SPOT;

	// This is a cache of the integrated covariance.
	private double[][][]	integratedLIBORCovariance;

	public static class CalibrationItem {
		public final AbstractLIBORMonteCarloProduct		calibrationProduct;
		public final double								calibrationTargetValue;
		public final double								calibrationWeight;

		public CalibrationItem(AbstractLIBORMonteCarloProduct calibrationProduct, double calibrationTargetValue, double calibrationWeight) {
			super();
			this.calibrationProduct		= calibrationProduct;
			this.calibrationTargetValue	= calibrationTargetValue;
			this.calibrationWeight		= calibrationWeight;
		}
	}

	/**
	 * Creates a LIBOR Market Model for given covariance.
	 * 
	 * @param liborPeriodDiscretization The discretization of the interest rate curve into forward rates (tenor structure).
	 * @param forwardRateCurve The initial values for the forward rates.
	 * @param covarianceModel The covariance model to use.
	 */
	public LIBORMarketModelStandard(
			TimeDiscretizationInterface		liborPeriodDiscretization,
			ForwardCurveInterface			forwardRateCurve,
			AbstractLIBORCovarianceModel	covarianceModel
			) {
		this.liborPeriodDiscretization	= liborPeriodDiscretization;
		this.forwardRateCurve			= forwardRateCurve;
		this.covarianceModel			= covarianceModel;
	}

	/**
	 * Creates a LIBOR Market Model for given covariance.
	 * 
	 * @param liborPeriodDiscretization The discretization of the interest rate curve into forward rates (tenor structure).
	 * @param forwardRateCurve The initial values for the forward rates.
	 * @param discountCurve The discount curve to use. This will create an LMM model with a deterministic zero-spread discounting adjustment.
	 * @param covarianceModel The covariance model to use.
	 */
	public LIBORMarketModelStandard(
			TimeDiscretizationInterface		liborPeriodDiscretization,
			ForwardCurveInterface			forwardRateCurve,
			DiscountCurveInterface			discountCurve,
			AbstractLIBORCovarianceModel	covarianceModel
			) {
		this.liborPeriodDiscretization	= liborPeriodDiscretization;
		this.forwardRateCurve			= forwardRateCurve;
		this.discountCurve				= discountCurve;
		this.covarianceModel			= covarianceModel;
	}

	/**
	 * Creates a LIBOR Market Model using a given covariance model and calibrating this model
	 * to given swaption volatility data.
	 * 
	 * @param liborPeriodDiscretization The discretization of the interest rate curve into forward rates (tenor structure).
	 * @param forwardRateCurve The initial values for the forward rates.
	 * @param covarianceModel The covariance model to use.
	 * @param swaptionMarketData The set of swaption values to calibrate to.
     * @throws net.finmath.exception.CalculationException Thrown if the valuation fails, specific cause may be available via the <code>cause()</code> method.
	 */
	public LIBORMarketModelStandard(
			TimeDiscretizationInterface			liborPeriodDiscretization,
			ForwardCurveInterface				forwardRateCurve,
			AbstractLIBORCovarianceModel		covarianceModel,
			AbstractSwaptionMarketData			swaptionMarketData
			) throws CalculationException {
		this(liborPeriodDiscretization, forwardRateCurve, null, covarianceModel, getCalibrationItems(liborPeriodDiscretization, forwardRateCurve, swaptionMarketData));
	}

	/**
	 * Creates a LIBOR Market Model for given covariance.
	 * 
	 * @param liborPeriodDiscretization The discretization of the interest rate curve into forward rates (tenor structure).
	 * @param forwardRateCurve The initial values for the forward rates.
	 * @param discountCurve The discount curve to use. This will create an LMM model with a deterministic zero-spread discounting adjustment.
	 * @param covarianceModel The covariance model to use.
	 * @param swaptionMarketData The set of swaption values to calibrate to.
     * @throws net.finmath.exception.CalculationException Thrown if the valuation fails, specific cause may be available via the <code>cause()</code> method.
	 */
	public LIBORMarketModelStandard(
			TimeDiscretizationInterface			liborPeriodDiscretization,
			ForwardCurveInterface				forwardRateCurve,
			DiscountCurveInterface				discountCurve,
			AbstractLIBORCovarianceModel		covarianceModel,
			AbstractSwaptionMarketData			swaptionMarketData
			) throws CalculationException {
		this(liborPeriodDiscretization, forwardRateCurve, discountCurve, covarianceModel, getCalibrationItems(liborPeriodDiscretization, forwardRateCurve, swaptionMarketData));
	}



	/**
	 * Creates a LIBOR Market Model for given covariance.
	 * 
	 * @param liborPeriodDiscretization The discretization of the interest rate curve into forward rates (tenor structure).
	 * @param forwardRateCurve The initial values for the forward rates.
	 * @param discountCurve The discount curve to use. This will create an LMM model with a deterministic zero-spread discounting adjustment.
	 * @param covarianceModel The covariance model to use.
	 * @param calibrationItems The vector of calibration items (a union of a product, target value and weight) for the objective function sum weight(i) * (modelValue(i)-targetValue(i).
     * @throws net.finmath.exception.CalculationException Thrown if the valuation fails, specific cause may be available via the <code>cause()</code> method.
	 */
	public LIBORMarketModelStandard(
			TimeDiscretizationInterface				liborPeriodDiscretization,
			ForwardCurveInterface					forwardRateCurve,
			DiscountCurveInterface					discountCurve,
			AbstractLIBORCovarianceModel			covarianceModel,
			CalibrationItem[]						calibrationItems
			) throws CalculationException {
		this.liborPeriodDiscretization	= liborPeriodDiscretization;

		double[] times = new double[liborPeriodDiscretization.getNumberOfTimeSteps()];
		for(int i=0; i<times.length; i++) times[i] = liborPeriodDiscretization.getTime(i);

		AbstractLIBORCovarianceModelParametric covarianceModelParametric = null;
		try {
			covarianceModelParametric = (AbstractLIBORCovarianceModelParametric)covarianceModel;
		}
		catch(Exception e) {
			throw new ClassCastException("Calibration is currently restricted to parametric covariance models (AbstractLIBORCovarianceModelParametric).");
		}

		this.forwardRateCurve	= forwardRateCurve;
		this.discountCurve		= discountCurve;

		// @TODO Should be more elegant. Convert array for constructor
		AbstractLIBORMonteCarloProduct[]	calibrationProducts		= new AbstractLIBORMonteCarloProduct[calibrationItems.length];
		double[]							calibrationTargetValues	= new double[calibrationItems.length];
		double[]							calibrationWeights		= new double[calibrationItems.length];
		for(int i=0; i<calibrationTargetValues.length; i++) {
			calibrationProducts[i]		= calibrationItems[i].calibrationProduct;
			calibrationTargetValues[i]	= calibrationItems[i].calibrationTargetValue;
			calibrationWeights[i]		= calibrationItems[i].calibrationWeight;
		}

		this.covarianceModel    = covarianceModelParametric.getCloneCalibrated(this, calibrationProducts, calibrationTargetValues, calibrationWeights);
	}

	private static CalibrationItem[] getCalibrationItems(TimeDiscretizationInterface liborPeriodDiscretization, ForwardCurveInterface forwardCurve, AbstractSwaptionMarketData swaptionMarketData) {
		if(swaptionMarketData == null) return null;
		
		TimeDiscretizationInterface	optionMaturities		= swaptionMarketData.getOptionMaturities();
		TimeDiscretizationInterface	tenor					= swaptionMarketData.getTenor();
		double						swapPeriodLength		= swaptionMarketData.getSwapPeriodLength();

		ArrayList<CalibrationItem> calibrationItems = new ArrayList<CalibrationItem>();
		for(int exerciseIndex=0; exerciseIndex<=optionMaturities.getNumberOfTimeSteps(); exerciseIndex++) {
			for(int tenorIndex=0; tenorIndex<=tenor.getNumberOfTimeSteps()-exerciseIndex; tenorIndex++) {

				// Create a swaption
				double exerciseDate	= optionMaturities.getTime(exerciseIndex);
				double swapLength	= tenor.getTime(tenorIndex);

				if(liborPeriodDiscretization.getTimeIndex(exerciseDate) < 0) continue;
				if(liborPeriodDiscretization.getTimeIndex(exerciseDate+swapLength) <= liborPeriodDiscretization.getTimeIndex(exerciseDate)) continue;

				int numberOfPeriods = (int)(swapLength / swapPeriodLength);

				double[] fixingDates      = new double[numberOfPeriods];
				double[] paymentDates     = new double[numberOfPeriods];
				double[] swapTenorTimes   = new double[numberOfPeriods+1];

				for(int periodStartIndex=0; periodStartIndex<numberOfPeriods; periodStartIndex++) {
					fixingDates[periodStartIndex] = exerciseDate + periodStartIndex * swapPeriodLength;
					paymentDates[periodStartIndex] = exerciseDate + (periodStartIndex+1) * swapPeriodLength;
					swapTenorTimes[periodStartIndex] = exerciseDate + periodStartIndex * swapPeriodLength;
				}
				swapTenorTimes[numberOfPeriods] = exerciseDate + numberOfPeriods * swapPeriodLength;


				// Swaptions swap rate
				ScheduleInterface swapTenor = new RegularSchedule(new TimeDiscretization(swapTenorTimes));
				double swaprate = Swap.getForwardSwapRate(swapTenor, swapTenor, forwardCurve, null);

				// Set swap rates for each period
				double[] swaprates        = new double[numberOfPeriods];
				for(int periodStartIndex=0; periodStartIndex<numberOfPeriods; periodStartIndex++) {
					swaprates[periodStartIndex] = swaprate;
				}

				if(isUseAnalyticApproximation) {
					AbstractLIBORMonteCarloProduct swaption = new SwaptionAnalyticApproximation(swaprate, swapTenorTimes, SwaptionAnalyticApproximation.ValueUnit.VOLATILITY);
					double impliedVolatility = swaptionMarketData.getVolatility(exerciseDate, swapLength, swaptionMarketData.getSwapPeriodLength(), swaprate);

					calibrationItems.add(new CalibrationItem(swaption, impliedVolatility, 1.0));
				}
				else {
					AbstractLIBORMonteCarloProduct swaption = new SwaptionSimple(swaprate, swapTenorTimes, SwaptionSimple.ValueUnit.VALUE);

					double forwardSwaprate		= Swap.getForwardSwapRate(swapTenor, swapTenor, forwardCurve);
					double swapAnnuity 			= SwapAnnuity.getSwapAnnuity(swapTenor, forwardCurve);
					double impliedVolatility	= swaptionMarketData.getVolatility(exerciseDate, swapLength, swaptionMarketData.getSwapPeriodLength(), swaprate);

					double targetValue = AnalyticFormulas.blackModelSwaptionValue(forwardSwaprate, impliedVolatility, exerciseDate, swaprate, swapAnnuity);

					calibrationItems.add(new CalibrationItem(swaption, targetValue, 1.0));
				}
			}
		}

		return calibrationItems.toArray(new CalibrationItem[calibrationItems.size()]);
	}

	/**
	 * Return the numeraire at a given time.
	 * The numeraire is provided for interpolated points. If requested on points which are not
	 * part of the tenor discretization, the numeraire uses a linear interpolation of the reciprocal
	 * value. See ISBN 0470047224 for details.
	 * 
	 * @param time Time time <i>t</i> for which the numeraire should be returned <i>N(t)</i>.
	 * @return The numeraire at the specified time as <code>RandomVariable</code>
     * @throws net.finmath.exception.CalculationException Thrown if the valuation fails, specific cause may be available via the <code>cause()</code> method.
	 */
	@Override
	public RandomVariableInterface getNumeraire(double time) throws CalculationException {
		int timeIndex = getLiborPeriodIndex(time);
		
		if(timeIndex < 0) {
			// Interpolation of Numeraire: linear interpolation of the reciprocal.
			int lowerIndex = -timeIndex -1;
			int upperIndex = -timeIndex;
			double alpha = (time-getLiborPeriod(lowerIndex)) / (getLiborPeriod(upperIndex) - getLiborPeriod(lowerIndex));
			return getNumeraire(getLiborPeriod(upperIndex)).invert().mult(alpha).add(getNumeraire(getLiborPeriod(lowerIndex)).invert().mult(1.0-alpha)).invert();
		}

		// Calculate the numeraire, when time is part of liborPeriodDiscretization

		// Get the start of the product
		int firstLiborIndex		= getLiborPeriodIndex(time);
		if(firstLiborIndex < 0) {
			throw new CalculationException("Simulation time discretization not part of forward rate tenor discretization.");
		}

		// Get the end of the product
		int lastLiborIndex 	= liborPeriodDiscretization.getNumberOfTimeSteps()-1;

		if(measure == Measure.SPOT) {
			// Spot measure
			firstLiborIndex	= 0;
			lastLiborIndex	= getLiborPeriodIndex(time)-1;
		}

		/*
		 * Calculation of the numeraire
		 */

		// Initialize to 1.0
		RandomVariableInterface numeraire = new RandomVariable(time, 1.0);

		// The product 
		for(int liborIndex = firstLiborIndex; liborIndex<=lastLiborIndex; liborIndex++) {
			RandomVariableInterface libor = getLIBOR(getTimeIndex(Math.min(time,liborPeriodDiscretization.getTime(liborIndex))), liborIndex);

			double periodLength = liborPeriodDiscretization.getTimeStep(liborIndex);

			if(measure == Measure.SPOT) {
				numeraire = numeraire.accrue(libor, periodLength);
			}
			else {
				numeraire = numeraire.discount(libor, periodLength);
			}
		}

		/*
		 * Adjust for discounting
		 */
		if(discountCurve != null) {
			DiscountCurveInterface discountcountCurveFromForwardPerformance = new DiscountCurveFromForwardCurve(forwardRateCurve);
			double deterministicNumeraireAdjustment = discountcountCurveFromForwardPerformance.getDiscountFactor(time) / discountCurve.getDiscountFactor(time);
			numeraire = numeraire.mult(deterministicNumeraireAdjustment);
		}
		return numeraire;
	}

	@Override
	public RandomVariableInterface[] getInitialState() {
		double[] liborInitialStates = new double[liborPeriodDiscretization.getNumberOfTimeSteps()];
		for(int timeIndex=0; timeIndex<liborPeriodDiscretization.getNumberOfTimeSteps(); timeIndex++) {
			double rate = forwardRateCurve.getForward(null, liborPeriodDiscretization.getTime(timeIndex));
			liborInitialStates[timeIndex] = Math.log(rate);
		}

		RandomVariableInterface[] initialStateRandomVariable = new RandomVariableInterface[getNumberOfComponents()];
		for(int componentIndex=0; componentIndex<getNumberOfComponents(); componentIndex++) {
			initialStateRandomVariable[componentIndex] = new RandomVariable(liborInitialStates[componentIndex]);
		}
		return initialStateRandomVariable;
	}

	/**
	 * Return the complete vector of the drift for the time index timeIndex, given that current state is realizationAtTimeIndex.
	 * Note: The random variable returned is a defensive copy and may be modified.
	 * The drift will be zero for rates being already fixed.
	 * 
	 * @see net.finmath.montecarlo.interestrate.LIBORMarketModelStandard#getNumeraire(double) The calculation of the drift is consistent with the calculation of the numeraire in <code>getNumeraire</code>.
	 * 
	 * @param timeIndex Time index <i>i</i> for which the drift should be returned <i>μ(t<sub>i</sub>)</i>.
	 * @param realizationAtTimeIndex Time current forward rate vector at time index <i>i</i> which should be used in the calculation.
	 * @return The drift vector μ(t<sub>i</sub>) as <code>RandomVariable[]</code>
	 */
	@Override
	public RandomVariableInterface[] getDrift(int timeIndex, RandomVariableInterface[] realizationAtTimeIndex, RandomVariableInterface[] realizationPredictor) {
		double	time				= getTime(timeIndex);
		int		firstLiborIndex		= this.getLiborPeriodIndex(time)+1;
		if(firstLiborIndex<0) firstLiborIndex = -firstLiborIndex-1 + 1;

		// Allocate drift vector and initialize to zero (will be used to sum up drift components)
		RandomVariableInterface[]	drift = new RandomVariableInterface[getNumberOfComponents()];
		RandomVariableInterface[][]	covarianceFactorSums	= new RandomVariableInterface[getNumberOfComponents()][getNumberOfFactors()];
		for(int componentIndex=firstLiborIndex; componentIndex<getNumberOfComponents(); componentIndex++) {
			drift[componentIndex] = new RandomVariable(0.0);
		}

		// Calculate drift for the component componentIndex (starting at firstLiborIndex, others are zero)
		for(int componentIndex=firstLiborIndex; componentIndex<getNumberOfComponents(); componentIndex++) {
			double						periodLength		= liborPeriodDiscretization.getTimeStep(componentIndex);
			RandomVariableInterface libor = realizationAtTimeIndex[componentIndex];
			RandomVariableInterface oneStepMeasureTransform = libor.discount(libor, periodLength).mult(periodLength);

			//oneStepMeasureTransform = oneStepMeasureTransform.mult(libor);

			RandomVariableInterface[]	factorLoading   	= getFactorLoading(timeIndex, componentIndex, realizationAtTimeIndex);
			RandomVariableInterface[]   covarianceFactors   = new RandomVariableInterface[getNumberOfFactors()];
			for(int factorIndex=0; factorIndex<getNumberOfFactors(); factorIndex++) {
				covarianceFactors[factorIndex] = factorLoading[factorIndex].mult(oneStepMeasureTransform);
				covarianceFactorSums[componentIndex][factorIndex] = covarianceFactors[factorIndex];
				if(componentIndex > firstLiborIndex)
					covarianceFactorSums[componentIndex][factorIndex] = covarianceFactorSums[componentIndex][factorIndex].add(covarianceFactorSums[componentIndex-1][factorIndex]);
			}
			for(int factorIndex=0; factorIndex<getNumberOfFactors(); factorIndex++) {
				drift[componentIndex] = drift[componentIndex].addProduct(covarianceFactorSums[componentIndex][factorIndex], factorLoading[factorIndex]);
			}
		}

		// Above is the drift for the spot measure: a simple conversion makes it the drift of the terminal measure.
		if(measure == Measure.TERMINAL) {
			for(int componentIndex=firstLiborIndex; componentIndex<getNumberOfComponents(); componentIndex++) {
				drift[componentIndex] = drift[componentIndex].sub(drift[getNumberOfComponents()-1]);
			}
		}

		// Drift adjustment for log-coordinate in each component
		for(int componentIndex=firstLiborIndex; componentIndex<getNumberOfComponents(); componentIndex++) {
			RandomVariableInterface		variance		= covarianceModel.getCovariance(timeIndex, componentIndex, componentIndex, realizationAtTimeIndex);
			drift[componentIndex] = drift[componentIndex].addProduct(variance, -0.5);
		}

		return drift;
	}


	@Override
	public	RandomVariableInterface[]	getFactorLoading(int timeIndex, int componentIndex, RandomVariableInterface[] realizationAtTimeIndex)
	{
		return covarianceModel.getFactorLoading(timeIndex, componentIndex, realizationAtTimeIndex);
	}

	@Override
	public RandomVariableInterface applyStateSpaceTransform(int componentIndex, RandomVariableInterface randomVariable) {
		return randomVariable.exp();
	}


	/**
	 * @return Returns the driftApproximationMethod.
	 */
	public Driftapproximation getDriftApproximationMethod() {
		return driftApproximationMethod;
	}

	@Override
	public RandomVariableInterface getLIBOR(double time, double periodStart, double periodEnd) throws CalculationException
	{
		int periodStartIndex    = getLiborPeriodIndex(periodStart);
		int periodEndIndex      = getLiborPeriodIndex(periodEnd);

		// The forward rates are provided on fractional tenor discretization points using linear interpolation. See ISBN 0470047224.

		// Interpolation on tenor, consistent with interpolation on numeraire (log-linear): interpolate end date
		if(periodEndIndex < 0) {
			int		previousEndIndex	= (-periodEndIndex-1)-1;
			double	previousEndTime		= getLiborPeriod(previousEndIndex);
			double	nextEndTime			= getLiborPeriod(previousEndIndex+1);
			RandomVariableInterface liborLongPeriod		= getLIBOR(time, periodStart, nextEndTime);
			RandomVariableInterface	liborShortPeriod	= getLIBOR(time, previousEndTime, nextEndTime);

			// Interpolate libor from periodStart to periodEnd on periodEnd
			RandomVariableInterface libor = liborLongPeriod.mult(nextEndTime-periodStart).add(1.0)
					.div(
							liborShortPeriod.mult(nextEndTime-previousEndTime).add(1.0).log().mult((nextEndTime-periodEnd)/(nextEndTime-previousEndTime)).exp()
							).sub(1.0).div(periodEnd-periodStart);

			// Analytic adjustment for the interpolation
			// @TODO reference to AnalyticModel must not be null
			// @TODO This adjustment only applies if the corresponding adjustment in getNumeraire is enabled
			double analyticLibor				= getForwardRateCurve().getForward(getAnalyticModel(), previousEndTime, periodEnd-previousEndTime);
			double analyticLiborShortPeriod		= getForwardRateCurve().getForward(getAnalyticModel(), previousEndTime, nextEndTime-previousEndTime);
			double analyticInterpolatedOnePlusLiborDt		= (1 + analyticLiborShortPeriod * (nextEndTime-previousEndTime)) / Math.exp(Math.log(1 + analyticLiborShortPeriod * (nextEndTime-previousEndTime)) * (nextEndTime-periodEnd)/(nextEndTime-previousEndTime));
			double analyticOnePlusLiborDt					= (1 + analyticLibor * (periodEnd-previousEndTime));
			double adjustment = analyticOnePlusLiborDt / analyticInterpolatedOnePlusLiborDt;
			libor = libor.mult(periodEnd-periodStart).add(1.0).mult(adjustment).sub(1.0).div(periodEnd-periodStart);
			return libor;
		}

		// Interpolation on tenor, consistent with interpolation on numeraire (log-linear): interpolate start date
		if(periodStartIndex < 0) {
			int		previousStartIndex	= (-periodStartIndex-1)-1;
			double	previousStartTime	= getLiborPeriod(previousStartIndex);
			double	nextStartTime		= getLiborPeriod(previousStartIndex+1);
			RandomVariableInterface liborLongPeriod		= getLIBOR(time, previousStartTime, periodEnd);
			RandomVariableInterface	liborShortPeriod	= getLIBOR(time, previousStartTime, nextStartTime);

			RandomVariableInterface libor = liborLongPeriod.mult(periodEnd-previousStartTime).add(1.0)
					.div(
							liborShortPeriod.mult(nextStartTime-previousStartTime).add(1.0).log().mult((periodStart-previousStartTime)/(nextStartTime-previousStartTime)).exp()
							).sub(1.0).div(periodEnd-periodStart);

			// Analytic adjustment for the interpolation
			// @TODO reference to AnalyticModel must not be null
			// @TODO This adjustment only applies if the corresponding adjustment in getNumeraire is enabled
			double analyticLibor				= getForwardRateCurve().getForward(getAnalyticModel(), previousStartTime, nextStartTime-periodStart);
			double analyticLiborShortPeriod		= getForwardRateCurve().getForward(getAnalyticModel(), previousStartTime, nextStartTime-previousStartTime);
			double analyticInterpolatedOnePlusLiborDt		= (1 + analyticLiborShortPeriod * (nextStartTime-previousStartTime)) / Math.exp(Math.log(1 + analyticLiborShortPeriod * (nextStartTime-previousStartTime)) * (nextStartTime-periodStart)/(nextStartTime-previousStartTime));
			double analyticOnePlusLiborDt					= (1 + analyticLibor * (periodStart-previousStartTime));
			double adjustment = analyticOnePlusLiborDt / analyticInterpolatedOnePlusLiborDt;
			libor = libor.mult(periodEnd-periodStart).add(1.0).div(adjustment).sub(1.0).div(periodEnd-periodStart);
			return libor;
		}

		if(periodStartIndex < 0 || periodEndIndex < 0) throw new AssertionError("LIBOR requested outside libor discretization points and interpolation was not performed.");

		// If time is beyond fixing, use the fixing time.
		time = Math.min(time, periodStart);
		int timeIndex           = getTimeIndex(time);

		// If time is not part of the discretization, use the latest available point.
		if(timeIndex < 0) {
			timeIndex = -timeIndex-2;
//			double timeStep = getTimeDiscretization().getTimeStep(timeIndex);
//			return getLIBOR(getTime(timeIndex), periodStart, periodEnd).mult((getTime(timeIndex+1)-time)/timeStep).add(getLIBOR(getTime(timeIndex+1), periodStart, periodEnd).mult((time-getTime(timeIndex))/timeStep));
		}

		// If this is a model primitive then return it
		if(periodStartIndex+1==periodEndIndex) return getLIBOR(timeIndex, periodStartIndex);

		// The requested LIBOR is not a model primitive. We need to calculate it (slow!)
		RandomVariableInterface accrualAccount = getProcess().getStochasticDriver().getRandomVariableForConstant(1.0);

		// Calculate the value of the forward bond
		for(int periodIndex = periodStartIndex; periodIndex<periodEndIndex; periodIndex++)
		{
			double subPeriodLength = getLiborPeriod(periodIndex+1) - getLiborPeriod(periodIndex);
			RandomVariableInterface liborOverSubPeriod = getLIBOR(timeIndex, periodIndex);

			accrualAccount = accrualAccount.accrue(liborOverSubPeriod, subPeriodLength);
		}

		RandomVariableInterface libor = accrualAccount.sub(1.0).div(periodEnd - periodStart);

		return libor;
	}

	@Override
	public RandomVariableInterface getLIBOR(int timeIndex, int liborIndex) throws CalculationException
	{
		// This method is just a synonym - call getProcessValue of super class
		return getProcessValue(timeIndex, liborIndex);
	}

	/**
	 * This method is just a synonym to getNumberOfLibors
	 * @return The number of components
	 */
	@Override
	public int getNumberOfComponents() {
		return getNumberOfLibors();
	}


	/* (non-Javadoc)
	 * @see net.finmath.montecarlo.interestrate.LIBORMarketModelInterface#getNumberOfLibors()
	 */
	@Override
	public int getNumberOfLibors()
	{
		// This is just a synonym to number of components
		return liborPeriodDiscretization.getNumberOfTimeSteps();
	}

	/* (non-Javadoc)
	 * @see net.finmath.montecarlo.interestrate.LIBORMarketModelInterface#getLiborPeriod(int)
	 */
	@Override
	public double getLiborPeriod(int timeIndex) {
		if(timeIndex >= liborPeriodDiscretization.getNumberOfTimes()) throw new ArrayIndexOutOfBoundsException("Index for LIBOR period discretization out of bounds.");
		return liborPeriodDiscretization.getTime(timeIndex);
	}

	/* (non-Javadoc)
	 * @see net.finmath.montecarlo.interestrate.LIBORMarketModelInterface#getLiborPeriodIndex(double)
	 */
	@Override
	public int getLiborPeriodIndex(double time) {
		return liborPeriodDiscretization.getTimeIndex(time);
	}

	/* (non-Javadoc)
	 * @see net.finmath.montecarlo.interestrate.LIBORMarketModelInterface#getLiborPeriodDiscretization()
	 */
	@Override
	public TimeDiscretizationInterface getLiborPeriodDiscretization() {
		return liborPeriodDiscretization;
	}

	/**
	 * Alternative implementation for the drift. For experimental purposes.
	 * 
	 * @param timeIndex
	 * @param componentIndex
	 * @param realizationAtTimeIndex
	 * @param realizationPredictor
	 * @return
	 */
	private RandomVariableInterface getDrift(int timeIndex, int componentIndex, RandomVariableInterface[] realizationAtTimeIndex, RandomVariableInterface[] realizationPredictor) {

		// Check if this LIBOR is already fixed
		if(getTime(timeIndex) >= this.getLiborPeriod(componentIndex)) {
			return null;
		}

		/*
		 * We implemented several different methods to calculate the drift
		 */
		if(driftApproximationMethod == Driftapproximation.PREDICTOR_CORRECTOR && realizationPredictor != null) {
			RandomVariableInterface drift					= getDriftEuler(timeIndex, componentIndex, realizationAtTimeIndex);
			RandomVariableInterface driftEulerWithPredictor	= getDriftEuler(timeIndex, componentIndex, realizationPredictor);
			drift = drift.add(driftEulerWithPredictor).div(2.0);

			return drift;
		}
		else if(driftApproximationMethod == Driftapproximation.LINE_INTEGRAL && realizationPredictor != null) {
			return getDriftLineIntegral(timeIndex, componentIndex, realizationAtTimeIndex, realizationPredictor);		    
		}
		else {
			return getDriftEuler(timeIndex, componentIndex, realizationAtTimeIndex);
		}		
	}

	protected RandomVariableInterface getDriftEuler(int timeIndex, int componentIndex, RandomVariableInterface[] liborVectorStart) {
		// The following is the drift of the LIBOR component
		double	time					= getTime(timeIndex);

		// Initialize to 0.0
		RandomVariableInterface drift = new RandomVariable(time, 0.0);

		// Get the start and end of the summation (start is the LIBOR after the current LIBOR component, end is the last LIBOR)
		int firstLiborIndex, lastLiborIndex;
		switch(measure) {
		case SPOT:
			// Spot measure
			firstLiborIndex	= this.getLiborPeriodIndex(time)+1;
			if(firstLiborIndex<0) firstLiborIndex = -firstLiborIndex-1 + 1;
			lastLiborIndex	= componentIndex;
			break;
		case TERMINAL:
		default:
			firstLiborIndex	= componentIndex+1;
			lastLiborIndex 	= liborPeriodDiscretization.getNumberOfTimeSteps()-1;
			break;
		}

		// The sum
		for(int liborIndex = firstLiborIndex; liborIndex<=lastLiborIndex; liborIndex++) {
			double						periodLength	= liborPeriodDiscretization.getTimeStep(liborIndex);
			RandomVariableInterface		covariance		= covarianceModel.getCovariance(timeIndex, componentIndex, liborIndex, null);
			RandomVariableInterface libor			= liborVectorStart[liborIndex];
			covariance = covariance.mult(periodLength).mult(libor).discount(libor, periodLength);
			drift = drift.add(covariance);
		}
		if(measure == Measure.TERMINAL) {
			drift = drift.mult(-1.0);
		}

		// Drift adjustment for log-coordinate
		RandomVariableInterface		variance		= covarianceModel.getCovariance(timeIndex, componentIndex, componentIndex, null);
		drift = drift.addProduct(variance, -0.5);

		return drift;
	}

	private RandomVariableInterface getDriftLineIntegral(int timeIndex, int componentIndex, RandomVariableInterface[] liborVectorStart, RandomVariableInterface[] liborVectorEnd) {
		// The following is the dirft of the LIBOR component

		double	time				= getTime(timeIndex);

		// Check if this LIBOR is already fixed
		if(getTime(timeIndex) >= this.getLiborPeriod(componentIndex)) {
			return null;
		}

		// Initialize to 0.0
		RandomVariableInterface drift = new RandomVariable(time, 0.0);

		// Get the start and end of the summation (start is the LIBOR after the current LIBOR component, end is the last LIBOR)
		int firstLiborIndex, lastLiborIndex;
		switch(measure) {
		case SPOT:
			// Spot measure
			firstLiborIndex	= this.getLiborPeriodIndex(time)+1;
			if(firstLiborIndex<0) firstLiborIndex = -firstLiborIndex-1 + 1;
			lastLiborIndex	= componentIndex;
			break;
		case TERMINAL:
		default:
			firstLiborIndex	= componentIndex+1;
			lastLiborIndex 	= liborPeriodDiscretization.getNumberOfTimeSteps()-1;
			break;
		}

		// The sum
		for(int liborIndex = firstLiborIndex; liborIndex<=lastLiborIndex; liborIndex++) {

			double periodLength = liborPeriodDiscretization.getTimeStep(liborIndex);
			RandomVariableInterface	covariance	= covarianceModel.getCovariance(timeIndex, componentIndex, liborIndex, null);

			/*
			 * We calculate
			 * driftTerm = covariance * log( (1 + periodLength * liborVectorEnd[liborIndex]) / (1 + periodLength * liborVectorStart[liborIndex]) )
			 *            / log(liborVectorEnd[liborIndex] / liborVectorStart[liborIndex])
			 */

			RandomVariableInterface driftTerm = new RandomVariable(1.0);
			driftTerm = driftTerm.accrue(liborVectorEnd[liborIndex], periodLength);
			driftTerm = driftTerm.discount(liborVectorStart[liborIndex], periodLength);
			driftTerm = driftTerm.log();
			driftTerm = driftTerm.mult(covariance);
			driftTerm = driftTerm.div(liborVectorEnd[liborIndex].div(liborVectorStart[liborIndex]).log());

			drift = drift.sub(driftTerm);
		}

		return drift;
	}

	/**
	 * @return Returns the measure.
	 */
	public Measure getMeasure() {
		return measure;
	}

	/* (non-Javadoc)
	 * @see net.finmath.montecarlo.interestrate.LIBORMarketModelInterface#getIntegratedLIBORCovariance()
	 */
	@Override
	public synchronized double[][][] getIntegratedLIBORCovariance() {
		if(integratedLIBORCovariance != null) return integratedLIBORCovariance;

		TimeDiscretizationInterface liborPeriodDiscretization = getLiborPeriodDiscretization();
		TimeDiscretizationInterface simulationTimeDiscretization = getTimeDiscretization();

		integratedLIBORCovariance = new double[simulationTimeDiscretization.getNumberOfTimeSteps()][liborPeriodDiscretization.getNumberOfTimeSteps()][liborPeriodDiscretization.getNumberOfTimeSteps()];
		for(int componentIndex1 = 0; componentIndex1 < liborPeriodDiscretization.getNumberOfTimeSteps(); componentIndex1++) {
			// Sum the libor cross terms (use symmetry)
			for(int componentIndex2 = componentIndex1; componentIndex2 < liborPeriodDiscretization.getNumberOfTimeSteps(); componentIndex2++) {
				double integratedLIBORCovarianceValue = 0.0;
				for(int timeIndex = 0; timeIndex < simulationTimeDiscretization.getNumberOfTimeSteps(); timeIndex++) {
					double dt = getTime(timeIndex+1) - getTime(timeIndex);
					RandomVariableInterface[] factorLoadingOfComponent1 = getCovarianceModel().getFactorLoading(timeIndex, componentIndex1, null);
					RandomVariableInterface[] factorLoadingOfComponent2 = getCovarianceModel().getFactorLoading(timeIndex, componentIndex2, null);
					for(int factorIndex = 0; factorIndex < getNumberOfFactors(); factorIndex++) {
						integratedLIBORCovarianceValue += factorLoadingOfComponent1[factorIndex].get(0) * factorLoadingOfComponent2[factorIndex].get(0) * dt;
					}
					integratedLIBORCovariance[timeIndex][componentIndex1][componentIndex2] = integratedLIBORCovarianceValue;
				}
			}
		}

		return integratedLIBORCovariance;
	}

	@Override
	public Object clone() {
		return new LIBORMarketModelStandard(liborPeriodDiscretization, forwardRateCurve, covarianceModel);
	}

	/**
	 * @param driftApproximationMethod The driftApproximationMethod to set.
	 */
	public void setDriftApproximationMethod(Driftapproximation driftApproximationMethod) {
		this.driftApproximationMethod = driftApproximationMethod;
	}

	/**
	 * @param measure The measure to set.
	 */
	public void setMeasure(Measure measure) {
		this.measure = measure;
	}

	@Override
	public AnalyticModelInterface getAnalyticModel() {
		return curveModel;
	}

	@Override
	public DiscountCurveInterface getDiscountCurve() {
		if(discountCurve == null) {
			DiscountCurveInterface discountCurveFromForwardCurve = new DiscountCurveFromForwardCurve(getForwardRateCurve());
			return discountCurveFromForwardCurve;
		}

		return discountCurve;
	}

	@Override
	public ForwardCurveInterface getForwardRateCurve() {
		return forwardRateCurve;
	}

	/**
	 * Return the swaption market data used for calibration (if any, may be null).
	 * 
	 * @return The swaption market data used for calibration (if any, may be null).
	 */
	public AbstractSwaptionMarketData getSwaptionMarketData() {
		return swaptionMarketData;
	}

	/* (non-Javadoc)
	 * @see net.finmath.montecarlo.interestrate.LIBORMarketModelInterface#getCovarianceModel()
	 */
	@Override
	public AbstractLIBORCovarianceModel getCovarianceModel() {
		return covarianceModel;
	}

	/**
	 * @param covarianceModel A covariance model
	 * @return A new <code>LIBORMarketModelStandard</code> using the specified covariance model.
	 */
	@Override
	public LIBORMarketModelStandard getCloneWithModifiedCovarianceModel(AbstractLIBORCovarianceModel covarianceModel) {
		LIBORMarketModelStandard model = (LIBORMarketModelStandard)this.clone();
		model.covarianceModel = covarianceModel;
		return model;
	}

	@Override
	public LIBORMarketModel getCloneWithModifiedData(Map<String, Object> dataModified) throws CalculationException {
		TimeDiscretizationInterface		liborPeriodDiscretization	= this.liborPeriodDiscretization;
		AnalyticModelInterface			analyticModel				= this.curveModel;
		ForwardCurveInterface			forwardRateCurve			= this.forwardRateCurve;
		AbstractLIBORCovarianceModel	covarianceModel				= this.covarianceModel;
		AbstractSwaptionMarketData		swaptionMarketData			= null;

		if(dataModified.containsKey("liborPeriodDiscretization")) {
			liborPeriodDiscretization = (TimeDiscretizationInterface)dataModified.get("liborPeriodDiscretization");
		}
		if(dataModified.containsKey("forwardRateCurve")) {
			forwardRateCurve = (ForwardCurveInterface)dataModified.get("forwardRateCurve");
		}
		if(dataModified.containsKey("forwardRateShift")) {
			throw new RuntimeException("Forward rate shift clone currently disabled.");
		}
		if(dataModified.containsKey("covarianceModel")) {
			covarianceModel = (AbstractLIBORCovarianceModel)dataModified.get("covarianceModel");
		}
		if(dataModified.containsKey("swaptionMarketData")) {
			swaptionMarketData = (AbstractSwaptionMarketData)dataModified.get("swaptionMarketData");
		}

		if(swaptionMarketData == null) {
			return new LIBORMarketModel(liborPeriodDiscretization, forwardRateCurve, covarianceModel);
		}
		else {
			return new LIBORMarketModel(liborPeriodDiscretization, forwardRateCurve, covarianceModel, swaptionMarketData);

		}
	}
}