net.finmath.montecarlo.interestrate.LIBORMarketModel Maven / Gradle / Ivy

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/*
 * (c) Copyright Christian P. Fries, Germany. Contact: [email protected].
 *
 * Created on 09.02.2004
 */
package net.finmath.montecarlo.interestrate;

import java.util.ArrayList;
import java.util.HashMap;
import java.util.Map;
import java.util.concurrent.ConcurrentHashMap;

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.AbstractRandomVariableFactory;
import net.finmath.montecarlo.RandomVariableFactory;
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.montecarlo.process.AbstractProcessInterface;
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 (generalized) LIBOR market model with some drift approximation methods.
 * 


 * In its default case the class specifies a multi-factor LIBOR market model in its log-normal formulation, that is
 * L_j = exp(Y_j)  where
 * \[
 * 		dY_{j} = \mu_{j} dt + \lambda_{1,j} dW_{1} + \ldots + \lambda_{m,j} dW_{m}
 * \]
 * 

 * The model uses an AbstractLIBORCovarianceModel for the specification of
 * (λ_1,j,...,λ_m,j) as a covariance model.
 * See {@link net.finmath.montecarlo.model.AbstractModelInterface} for details on the implemented interface
 * 


 * However, the class is more general:
 * 
 * 	
 * 		The model may be log-normal or normal specification with a given local volatility.
 *	
 * 	
 * 		The class implements different measure(drift) / numeraire pairs: terminal measure and spot measure.
 *	
 * 	
 * 		The class allows to configure a discounting curve (e.g. for "OIS discounting") using a simple deterministic zero spread.
 * 		In this case, the numeraire \( N(t) \) is adjusted by \( \exp( \int_0^t -\lambda(\tau) d\tau ) \). 
 *	
 * 
 * 
 * 

 * The class specifies a LIBOR market model, that is
 * L_j = f(Y_j)  where
 * 
 * 	
 * 		f is f(x) = exp(x) (default, log-normal LIBOR Market Model) or
 * 	
 * 	
 * 		f is f(x) = x (normal model, used if property.set("stateSpace","NORMAL"))
 * 	
 * 
 * and
 * 

 * dY_j = μ_j dt + λ_1,j dW₁ + ... + λ_m,j dW_m 

 * 

 * see {@link net.finmath.montecarlo.model.AbstractModelInterface} for details on the implemented interface.
 * 

 * The model uses an AbstractLIBORCovarianceModel as a covariance model.
 * If the covariance model is of type AbstractLIBORCovarianceModelParametric
 * a calibration to swaptions can be performed.
 * 

 * Note that λ may still depend on L, hence generating a log-normal dynamic for L even
 * if the stateSpace property has been set to NORMAL.
 * 

 *
 * The map properties allows to configure the model. The following keys may be used:
 * 
 * 		
 * 			measure: Possible values:
 * 			
 * 				
 * 					SPOT: Simulate under spot measure. In this case, the single curve numeraire
 * 					is \( N(T_{i}) = \prod_{j=0}^{i-1} (1 + L(T_{j},T_{j+1};T_{j}) (T_{j+1}-T_{j})) \).
 * 				
 * 				
 * 					TERMINAL: Simulate under terminal measure. In this case, the single curve numeraire
 * 					is \( N(T_{i}) = P(T_{n};T_{i}) = \prod_{j=i}^{n-1} (1 + L(T_{j},T_{j+1};T_{i}) (T_{j+1}-T_{j}))^{-1} \).
 * 				
 *			
 *		
 * 		
 * 			stateSpace: Possible values:
 * 			
 * 				
 * 					LOGNORMAL: The state space transform is set to exp, i.e., L = exp(Y). When the covariance model is deterministic, then this is the classical lognormal LIBOR market model. Note that the covariance model may still provide a local volatility function.
 * 				
 * 				
 * 					NORMAL: The state space transform is set to identity, i.e., L = Y. When the covariance model is deterministic, then this is a normal LIBOR market model. Note that the covariance model may still provide a local volatility function.
 * 				
 *			
 *		
 * 		
 * 			liborCap: An optional Double value applied as a cap to the LIBOR rates.
 * 			May be used to limit the simulated valued to prevent values attaining POSITIVE_INFINITY and
 * 			numerical problems. To disable the cap, set liborCap to Double.POSITIVE_INFINITY.
 *		
 * 
 * 

 * The main task of this class is to calculate the risk-neutral drift and the
 * corresponding numeraire given the covariance model.
 * 
 * The calibration of the covariance structure is not part of this class. For the calibration
 * of parametric models of the instantaneous covariance see
 * {@link net.finmath.montecarlo.interestrate.modelplugins.AbstractLIBORCovarianceModelParametric#getCloneCalibrated(LIBORMarketModelInterface, AbstractLIBORMonteCarloProduct[], double[], double[], Map)}.
 * 
 * @author Christian Fries
 * @version 1.2
 * @see net.finmath.montecarlo.process.AbstractProcessInterface The interface for numerical schemes.
 * @see net.finmath.montecarlo.model.AbstractModelInterface The interface for models provinding parameters to numerical schemes.
 * @see net.finmath.montecarlo.interestrate.modelplugins.AbstractLIBORCovarianceModel The abstract covariance model plug ins.
 * @see net.finmath.montecarlo.interestrate.modelplugins.AbstractLIBORCovarianceModelParametric A parametic covariance model including a generic calibration algorithm.
 */
public class LIBORMarketModel extends AbstractModel implements LIBORMarketModelInterface {

	public enum Driftapproximation	{ EULER, LINE_INTEGRAL, PREDICTOR_CORRECTOR }
	public enum Measure				{ SPOT, TERMINAL }
	public enum StateSpace			{ NORMAL, LOGNORMAL }

	private final TimeDiscretizationInterface		liborPeriodDiscretization;

	private String							forwardCurveName;
	private AnalyticModelInterface			curveModel;

	private ForwardCurveInterface			forwardRateCurve;
	private DiscountCurveInterface			discountCurve;

	private final AbstractRandomVariableFactory	randomVariableFactory;
	private AbstractLIBORCovarianceModel	covarianceModel;

	private AbstractSwaptionMarketData		swaptionMarketData;

	private Driftapproximation	driftApproximationMethod	= Driftapproximation.EULER;
	private Measure				measure						= Measure.SPOT;
	private StateSpace			stateSpace					= StateSpace.LOGNORMAL;
	private double				liborCap					= 1E5;

	// This is a cache of the integrated covariance.
	private double[][][]	integratedLIBORCovariance;
	private final Object	integratedLIBORCovarianceLazyInitLock = new Object();

	// Cache for the numeraires, needs to be invalidated if process changes
	private final ConcurrentHashMap	numeraires;
	private AbstractProcessInterface									numerairesProcess = null;

	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;
		}

		@Override
		public String toString() {
			return "CalibrationItem [calibrationProduct=" + calibrationProduct
					+ ", calibrationTargetValue=" + calibrationTargetValue
					+ ", calibrationWeight=" + calibrationWeight + "]";
		}
	}

	/**
	 * Creates a LIBOR Market Model for given covariance.
	 * 

	 * If calibrationItems in non-empty and the covariance model is a parametric model,
	 * the covariance will be replaced by a calibrate version of the same model, i.e.,
	 * the LIBOR Market Model will be calibrated.
	 * 

	 * The map properties allows to configure the model. The following keys may be used:
	 * 
	 * 		
	 * 			measure: Possible values:
	 * 			
	 * 				
	 * 					SPOT (String): Simulate under spot measure.
	 * 				
	 * 				
	 * 					TERMINAL (String): Simulate under terminal measure.
	 * 				
	 *			
	 *		
	 * 		
	 * 			stateSpace: Possible values:
	 * 			
	 * 				
	 * 					LOGNORMAL (String): Simulate L = exp(Y).
	 * 				
	 * 				
	 * 					NORMAL (String): Simulate L = Y.
	 * 				
	 *			
	 *		
	 * 		
	 * 			liborCap: An optional Double value applied as a cap to the LIBOR rates.
	 * 			May be used to limit the simulated valued to prevent values attaining POSITIVE_INFINITY and
	 * 			numerical problems. To disable the cap, set liborCap to Double.POSITIVE_INFINITY.
	 *		
	 * 		
	 * 			calibrationParameters: Possible values:
	 * 			
	 * 				
	 * 					Map<String,Object> a parameter map with the following key/value pairs:
	 * 					
	 *				 		
	 * 							accuracy: Double specifying the required solver accuracy.
	 * 						
	 *				 		
	 * 							maxIterations: Integer specifying the maximum iterations for the solver.
	 * 						
	 *					
	 *				
	 *			
	 *		
	 * 
	 * 
	 * @param liborPeriodDiscretization The discretization of the interest rate curve into forward rates (tenor structure).
	 * @param analyticModel The associated analytic model of this model (containing the associated market data objects like curve).
	 * @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 randomVariableFactory The random variable factory used to create the inital values of the model.
	 * @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).
	 * @param properties Key value map specifying properties like measure and stateSpace.
	 * @throws net.finmath.exception.CalculationException Thrown if the valuation fails, specific cause may be available via the cause() method.
	 */
	public LIBORMarketModel(
			TimeDiscretizationInterface			liborPeriodDiscretization,
			AnalyticModelInterface				analyticModel,
			ForwardCurveInterface				forwardRateCurve,
			DiscountCurveInterface				discountCurve,
			AbstractRandomVariableFactory		randomVariableFactory,
			AbstractLIBORCovarianceModel		covarianceModel,
			CalibrationItem[]					calibrationItems,
			Map						properties
			) throws CalculationException {

		// Set some properties
		if(properties != null && properties.containsKey("measure"))					measure		= Measure.valueOf(((String)properties.get("measure")).toUpperCase());
		if(properties != null && properties.containsKey("stateSpace"))				stateSpace	= StateSpace.valueOf(((String)properties.get("stateSpace")).toUpperCase());
		if(properties != null && properties.containsKey("liborCap"))				liborCap	= (Double)properties.get("liborCap");

		Map calibrationParameters = null;
		if(properties != null && properties.containsKey("calibrationParameters"))	calibrationParameters	= (Map)properties.get("calibrationParameters");

		this.liborPeriodDiscretization	= liborPeriodDiscretization;
		this.curveModel					= analyticModel;
		this.forwardRateCurve		= forwardRateCurve;
		this.discountCurve			= discountCurve;
		this.randomVariableFactory	= randomVariableFactory;
		this.covarianceModel		= covarianceModel;

		double[] times = new double[liborPeriodDiscretization.getNumberOfTimeSteps()];
		for(int i=0; i 0) {
			AbstractLIBORCovarianceModelParametric covarianceModelParametric = null;
			try {
				covarianceModelParametric = (AbstractLIBORCovarianceModelParametric)covarianceModel;
			}
			catch(Exception e) {
				throw new ClassCastException("Calibration is currently restricted to parametric covariance models (AbstractLIBORCovarianceModelParametric).");
			}

			// @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();
	}

	/**
	 * Creates a LIBOR Market Model for given covariance.
	 * 

	 * If calibrationItems in non-empty and the covariance model is a parametric model,
	 * the covariance will be replaced by a calibrate version of the same model, i.e.,
	 * the LIBOR Market Model will be calibrated.
	 * 

	 * The map properties allows to configure the model. The following keys may be used:
	 * 
	 * 		
	 * 			measure: Possible values:
	 * 			
	 * 				
	 * 					SPOT (String): Simulate under spot measure.
	 * 				
	 * 				
	 * 					TERMINAL (String): Simulate under terminal measure.
	 * 				
	 *			
	 *		
	 * 		
	 * 			stateSpace: Possible values:
	 * 			
	 * 				
	 * 					LOGNORMAL (String): Simulate L = exp(Y).
	 * 				
	 * 				
	 * 					NORMAL (String): Simulate L = Y.
	 * 				
	 *			
	 *		
	 * 		
	 * 			liborCap: An optional Double value applied as a cap to the LIBOR rates.
	 * 			May be used to limit the simulated valued to prevent values attaining POSITIVE_INFINITY and
	 * 			numerical problems. To disable the cap, set liborCap to Double.POSITIVE_INFINITY.
	 *		
	 * 		
	 * 			calibrationParameters: Possible values:
	 * 			
	 * 				
	 * 					Map<String,Object> a parameter map with the following key/value pairs:
	 * 					
	 *				 		
	 * 							accuracy: Double specifying the required solver accuracy.
	 * 						
	 *				 		
	 * 							maxIterations: Integer specifying the maximum iterations for the solver.
	 * 						
	 *					
	 *				
	 *			
	 *		
	 * 
	 * 
	 * @param liborPeriodDiscretization The discretization of the interest rate curve into forward rates (tenor structure).
	 * @param analyticModel The associated analytic model of this model (containing the associated market data objects like curve).
	 * @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).
	 * @param properties Key value map specifying properties like measure and stateSpace.
	 * @throws net.finmath.exception.CalculationException Thrown if the valuation fails, specific cause may be available via the cause() method.
	 */
	public LIBORMarketModel(
			TimeDiscretizationInterface			liborPeriodDiscretization,
			AnalyticModelInterface				analyticModel,
			ForwardCurveInterface				forwardRateCurve,
			DiscountCurveInterface				discountCurve,
			AbstractLIBORCovarianceModel		covarianceModel,
			CalibrationItem[]					calibrationItems,
			Map						properties
			) throws CalculationException {
		this(liborPeriodDiscretization, analyticModel, forwardRateCurve, discountCurve, new RandomVariableFactory(), covarianceModel, calibrationItems, properties);
	}

	/**
	 * 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.
	 * @throws net.finmath.exception.CalculationException Thrown if the valuation fails, specific cause may be available via the cause() method.
	 */
	public LIBORMarketModel(
			TimeDiscretizationInterface		liborPeriodDiscretization,
			ForwardCurveInterface			forwardRateCurve,
			AbstractLIBORCovarianceModel	covarianceModel
			) throws CalculationException {
		this(liborPeriodDiscretization, forwardRateCurve, new DiscountCurveFromForwardCurve(forwardRateCurve), covarianceModel, new CalibrationItem[0], null);
	}

	/**
	 * 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.
	 * @throws net.finmath.exception.CalculationException Thrown if the valuation fails, specific cause may be available via the cause() method.
	 */
	public LIBORMarketModel(
			TimeDiscretizationInterface		liborPeriodDiscretization,
			ForwardCurveInterface			forwardRateCurve,
			DiscountCurveInterface			discountCurve,
			AbstractLIBORCovarianceModel	covarianceModel
			) throws CalculationException {
		this(liborPeriodDiscretization, forwardRateCurve, discountCurve, covarianceModel, new CalibrationItem[0], null);
	}

	/**
	 * 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 cause() method.
	 */
	public LIBORMarketModel(
			TimeDiscretizationInterface			liborPeriodDiscretization,
			ForwardCurveInterface				forwardRateCurve,
			AbstractLIBORCovarianceModel		covarianceModel,
			AbstractSwaptionMarketData			swaptionMarketData
			) throws CalculationException {
		this(liborPeriodDiscretization, forwardRateCurve, new DiscountCurveFromForwardCurve(forwardRateCurve), covarianceModel, swaptionMarketData, null);
	}

	/**
	 * 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 cause() method.
	 */
	public LIBORMarketModel(
			TimeDiscretizationInterface			liborPeriodDiscretization,
			ForwardCurveInterface				forwardRateCurve,
			DiscountCurveInterface				discountCurve,
			AbstractLIBORCovarianceModel		covarianceModel,
			AbstractSwaptionMarketData			swaptionMarketData
			) throws CalculationException {
		this(
				liborPeriodDiscretization,
				forwardRateCurve,
				discountCurve,
				covarianceModel,
				swaptionMarketData,
				null
				);
	}

	/**
	 * 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.
	 * @param properties Key value map specifying properties like measure and stateSpace.
	 * @throws net.finmath.exception.CalculationException Thrown if the valuation fails, specific cause may be available via the cause() method.
	 */
	public LIBORMarketModel(
			TimeDiscretizationInterface			liborPeriodDiscretization,
			ForwardCurveInterface				forwardRateCurve,
			DiscountCurveInterface				discountCurve,
			AbstractLIBORCovarianceModel		covarianceModel,
			AbstractSwaptionMarketData			swaptionMarketData,
			Map					properties
			) throws CalculationException {
		this(
				liborPeriodDiscretization,
				forwardRateCurve,
				discountCurve,
				covarianceModel,
				getCalibrationItems(
						liborPeriodDiscretization,
						forwardRateCurve,
						swaptionMarketData,
						// Condition under which we use analytic approximation
						(properties == null || properties.get("stateSpace") == null || ((String)properties.get("stateSpace")).toUpperCase().equals(StateSpace.LOGNORMAL.name()))
						&& AbstractLIBORCovarianceModelParametric.class.isAssignableFrom(covarianceModel.getClass())
						),
				properties
				);
	}



	/**
	 * Creates a LIBOR Market Model for given covariance.
	 * 

	 * If calibrationItems in non-empty and the covariance model is a parametric model,
	 * the covariance will be replaced by a calibrate version of the same model, i.e.,
	 * the LIBOR Market Model will be calibrated.
	 * 

	 * The map properties allows to configure the model. The following keys may be used:
	 * 
	 * 		
	 * 			measure: Possible values:
	 * 			
	 * 				
	 * 					SPOT (String): Simulate under spot measure.
	 * 				
	 * 				
	 * 					TERMINAL (String): Simulate under terminal measure.
	 * 				
	 *			
	 *		
	 * 		
	 * 			stateSpace: Possible values:
	 * 			
	 * 				
	 * 					LOGNORMAL (String): Simulate L = exp(Y).
	 * 				
	 * 				
	 * 					NORMAL (String): Simulate L = Y.
	 * 				
	 *			
	 *		
	 * 		
	 * 			calibrationParameters: Possible values:
	 * 			
	 * 				
	 * 					Map<String,Object> a parameter map with the following key/value pairs:
	 * 					
	 *				 		
	 * 							accuracy: Double specifying the required solver accuracy.
	 * 						
	 *				 		
	 * 							maxIterations: Integer specifying the maximum iterations for the solver.
	 * 						
	 *					
	 *				
	 *			
	 *		
	 * 
	 * 
	 * @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).
	 * @param properties Key value map specifying properties like measure and stateSpace.
	 * @throws net.finmath.exception.CalculationException Thrown if the valuation fails, specific cause may be available via the cause() method.
	 */
	public LIBORMarketModel(
			TimeDiscretizationInterface			liborPeriodDiscretization,
			ForwardCurveInterface				forwardRateCurve,
			DiscountCurveInterface				discountCurve,
			AbstractLIBORCovarianceModel		covarianceModel,
			CalibrationItem[]					calibrationItems,
			Map						properties
			) throws CalculationException {
		this(liborPeriodDiscretization, null, forwardRateCurve, discountCurve, covarianceModel, calibrationItems, properties);
	}

	private static CalibrationItem[] getCalibrationItems(TimeDiscretizationInterface liborPeriodDiscretization, ForwardCurveInterface forwardCurve, AbstractSwaptionMarketData swaptionMarketData, boolean isUseAnalyticApproximation) {
		if(swaptionMarketData == null) return null;

		TimeDiscretizationInterface	optionMaturities		= swaptionMarketData.getOptionMaturities();
		TimeDiscretizationInterface	tenor					= swaptionMarketData.getTenor();
		double						swapPeriodLength		= swaptionMarketData.getSwapPeriodLength();

		ArrayList calibrationItems = new ArrayList();
		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; periodStartIndext for which the numeraire should be returned N(t).
	 * @return The numeraire at the specified time as RandomVariableInterface
	 * @throws net.finmath.exception.CalculationException Thrown if the valuation fails, specific cause may be available via the cause() method.
	 */
	@Override
	public RandomVariableInterface getNumeraire(double time) throws CalculationException {
		int timeIndex = getLiborPeriodIndex(time);

		if(timeIndex < 0) {
			// Interpolation of Numeraire: log linear interpolation.
			int upperIndex = -timeIndex-1;
			int lowerIndex = upperIndex-1;
			if(lowerIndex < 0) throw new IllegalArgumentException("Numeraire requested for time " + time + ". Unsupported");

			double alpha = (time-getLiborPeriod(lowerIndex)) / (getLiborPeriod(upperIndex) - getLiborPeriod(lowerIndex));
			RandomVariableInterface numeraire = getNumeraire(getLiborPeriod(upperIndex)).log().mult(alpha).add(getNumeraire(getLiborPeriod(lowerIndex)).log().mult(1.0-alpha)).exp();

			/*
			 * Adjust for discounting, i.e. funding or collateralization
			 */
			if(discountCurve != null) {
				// This includes a control for zero bonds
				double deterministicNumeraireAdjustment = numeraire.invert().getAverage() / discountCurve.getDiscountFactor(curveModel, time);
				numeraire = numeraire.mult(deterministicNumeraireAdjustment);
			}

			return numeraire;
		}

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

		/*
		 * Check if numeraire cache is valid (i.e. process did not change)
		 */
		if(getProcess() != numerairesProcess) {
			numeraires.clear();
			numerairesProcess = getProcess();
		}

		/*
		 * Check if numeraire is part of the cache
		 */
		RandomVariableInterface numeraire = numeraires.get(timeIndex);
		if(numeraire == null) {
			/*
			 * Calculate the numeraire for timeIndex
			 */

			// Initialize to 1.0
			numeraire = getRandomVariableForConstant(1.0);


			// Get the start and end of the product
			int firstLiborIndex, lastLiborIndex;

			if(measure == Measure.TERMINAL) {
				firstLiborIndex	= getLiborPeriodIndex(time);
				if(firstLiborIndex < 0) {
					throw new CalculationException("Simulation time discretization not part of forward rate tenor discretization.");
				}

				lastLiborIndex 	= liborPeriodDiscretization.getNumberOfTimeSteps()-1;
			}
			else if(measure == Measure.SPOT) {
				// Spot measure
				firstLiborIndex	= 0;
				lastLiborIndex	= getLiborPeriodIndex(time)-1;
			}
			else {
				throw new CalculationException("Numeraire not implemented for specified measure.");
			}

			// 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);
				}
			}
			numeraires.put(timeIndex, numeraire);
		}

		/*
		 * Adjust for discounting, i.e. funding or collateralization
		 */
		if(discountCurve != null) {
			// This includes a control for zero bonds
			double deterministicNumeraireAdjustment = numeraire.invert().getAverage() / discountCurve.getDiscountFactor(curveModel, time);
			numeraire = numeraire.mult(deterministicNumeraireAdjustment);
		}
		return numeraire;
	}

	@Override
	public RandomVariableInterface[] getInitialState() {
		double[] liborInitialStates = new double[liborPeriodDiscretization.getNumberOfTimeSteps()];
		for(int timeIndex=0; timeIndexMeasure.SPOT or Measure.TERMINAL - depending how the
	 * model object was constructed. For Measure.TERMINAL the j-th entry of the return value is the random variable
	 * \[
	 * \mu_{j}^{\mathbb{Q}^{P(T_{n})}}(t) \ = \ - \mathop{\sum_{l\geq j+1}}_{l\leq n-1} \frac{\delta_{l}}{1+\delta_{l} L_{l}(t)} (\lambda_{j}(t) \cdot \lambda_{l}(t))
	 * \]
	 * and for Measure.SPOT the j-th entry of the return value is the random variable
	 * \[
	 * \mu_{j}^{\mathbb{Q}^{N}}(t) \ = \ \sum_{m(t) < l\leq j} \frac{\delta_{l}}{1+\delta_{l} L_{l}(t)} (\lambda_{j}(t) \cdot \lambda_{l}(t))
	 * \]
	 * where \( \lambda_{j} \) is the vector for factor loadings for the j-th component of the stochastic process (that is, the diffusion part is
	 * \( \sum_{k=1}^m \lambda_{j,k} \mathrm{d}W_{k} \)).
	 * 
	 * Note: The scalar product of the factor loadings determines the instantaneous covariance. If the model is written in log-coordinates (using exp as a state space transform), we find
	 * \(\lambda_{j} \cdot \lambda_{l} = \sum_{k=1}^m \lambda_{j,k} \lambda_{l,k} = \sigma_{j} \sigma_{l} \rho_{j,l} \).
	 * If the model is written without a state space transformation (in its orignial coordinates) then \(\lambda_{j} \cdot \lambda_{l} = \sum_{k=1}^m \lambda_{j,k} \lambda_{l,k} = L_{j} L_{l} \sigma_{j} \sigma_{l} \rho_{j,l} \).
	 * 
	 * 
	 * @see net.finmath.montecarlo.interestrate.LIBORMarketModel#getNumeraire(double) The calculation of the drift is consistent with the calculation of the numeraire in getNumeraire.
	 * @see net.finmath.montecarlo.interestrate.LIBORMarketModel#getFactorLoading(int, int, RandomVariableInterface[]) The factor loading \( \lambda_{j,k} \).
	 * 
	 * @param timeIndex Time index i for which the drift should be returned μ(t_i).
	 * @param realizationAtTimeIndex Time current forward rate vector at time index i which should be used in the calculation.
	 * @return The drift vector μ(t_i) as RandomVariable[]
	 */
	@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;

		RandomVariableInterface		zero	= getRandomVariableForConstant(0.0);

		// Allocate drift vector and initialize to zero (will be used to sum up drift components)
		RandomVariableInterface[]	drift = new RandomVariableInterface[getNumberOfComponents()];
		for(int componentIndex=firstLiborIndex; componentIndex=firstLiborIndex; componentIndex--) {
				double					periodLength	= liborPeriodDiscretization.getTimeStep(componentIndex);
				RandomVariableInterface libor			= realizationAtTimeIndex[componentIndex];
				RandomVariableInterface oneStepMeasureTransform = getRandomVariableForConstant(periodLength).discount(libor, periodLength);

				if(stateSpace == StateSpace.LOGNORMAL) oneStepMeasureTransform = oneStepMeasureTransform.mult(libor);

				RandomVariableInterface[]	factorLoading   	= getFactorLoading(timeIndex, componentIndex, realizationAtTimeIndex);
				for(int factorIndex=0; factorIndex= liborPeriodDiscretization.getNumberOfTimes() || timeIndex < 0) {
			throw new ArrayIndexOutOfBoundsException("Index for LIBOR period discretization out of bounds: " + timeIndex + ".");
		}
		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;
	}

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

	/* (non-Javadoc)
	 * @see net.finmath.montecarlo.interestrate.LIBORMarketModelInterface#getIntegratedLIBORCovariance()
	 */
	@Override
	public double[][][] getIntegratedLIBORCovariance() {
		synchronized (integratedLIBORCovarianceLazyInitLock) {
			if(integratedLIBORCovariance == null) {
				TimeDiscretizationInterface liborPeriodDiscretization = getLiborPeriodDiscretization();
				TimeDiscretizationInterface simulationTimeDiscretization = getCovarianceModel().getTimeDiscretization();

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

				// Integrate over time (i.e. sum up).
				for(int timeIndex = 1; timeIndex < simulationTimeDiscretization.getNumberOfTimeSteps(); timeIndex++) {
					double[][] prevIntegratedLIBORCovariance = integratedLIBORCovariance[timeIndex-1];
					double[][] thisIntegratedLIBORCovariance = integratedLIBORCovariance[timeIndex];
					for(int componentIndex1 = 0; componentIndex1 < liborPeriodDiscretization.getNumberOfTimeSteps(); componentIndex1++) {
						for(int componentIndex2 = componentIndex1; componentIndex2 < liborPeriodDiscretization.getNumberOfTimeSteps(); componentIndex2++) {
							thisIntegratedLIBORCovariance[componentIndex1][componentIndex2] = prevIntegratedLIBORCovariance[componentIndex1][componentIndex2] + thisIntegratedLIBORCovariance[componentIndex1][componentIndex2];
							thisIntegratedLIBORCovariance[componentIndex2][componentIndex1] = thisIntegratedLIBORCovariance[componentIndex1][componentIndex2];
						}
					}
				}
			}
		}

		return integratedLIBORCovariance;
	}

	@Override
	public Object clone() {
		try {
			Map properties = new HashMap();
			properties.put("measure",		measure.name());
			properties.put("stateSpace",	stateSpace.name());
			return new LIBORMarketModel(getLiborPeriodDiscretization(), getAnalyticModel(), getForwardRateCurve(), getDiscountCurve(), randomVariableFactory, covarianceModel, new CalibrationItem[0], properties);
		} catch (CalculationException e) {
			return null;
		}
	}

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

	@Override
	public DiscountCurveInterface getDiscountCurve() {
		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 LIBORMarketModel using the specified covariance model.
	 */
	@Override
	public LIBORMarketModel getCloneWithModifiedCovarianceModel(AbstractLIBORCovarianceModel covarianceModel) {
		LIBORMarketModel model = (LIBORMarketModel)this.clone();
		model.covarianceModel = covarianceModel;
		return model;
	}

	@Override
	public LIBORMarketModel getCloneWithModifiedData(Map dataModified) throws CalculationException {
		TimeDiscretizationInterface		liborPeriodDiscretization	= this.liborPeriodDiscretization;
		AnalyticModelInterface			analyticModel				= this.curveModel;
		ForwardCurveInterface			forwardRateCurve			= this.forwardRateCurve;
		DiscountCurveInterface			discountCurve				= this.discountCurve;
		AbstractLIBORCovarianceModel	covarianceModel				= this.covarianceModel;
		AbstractSwaptionMarketData		swaptionMarketData			= null;		// No recalibration, unless new swaption data is specified
		Map				properties					= new HashMap();
		properties.put("measure",		measure.name());
		properties.put("stateSpace",	stateSpace.name());

		if(dataModified.containsKey("liborPeriodDiscretization")) {
			liborPeriodDiscretization = (TimeDiscretizationInterface)dataModified.get("liborPeriodDiscretization");
		}
		if(dataModified.containsKey("forwardRateCurve")) {
			forwardRateCurve = (ForwardCurveInterface)dataModified.get("forwardRateCurve");
		}
		if(dataModified.containsKey("discountCurve")) {
			discountCurve = (DiscountCurveInterface)dataModified.get("discountCurve");
		}
		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");
		}

		LIBORMarketModel newModel = new LIBORMarketModel(liborPeriodDiscretization, forwardRateCurve, discountCurve, covarianceModel, swaptionMarketData, properties);
		newModel.curveModel = analyticModel;
		return newModel;
	}

	@Override
	public String toString() {
		return "LIBORMarketModel [liborPeriodDiscretization="
				+ liborPeriodDiscretization + ", forwardCurveName="
				+ forwardCurveName + ", curveModel=" + curveModel
				+ ", forwardRateCurve=" + forwardRateCurve + ", discountCurve="
				+ discountCurve + ", covarianceModel=" + covarianceModel
				+ ", driftApproximationMethod=" + driftApproximationMethod
				+ ", measure=" + measure + ", stateSpace=" + stateSpace + "]";
	}
}