SwaptionAnalyticApproximationRebonato.java

/*
 * (c) Copyright Christian P. Fries, Germany. Contact: email@christian-fries.de.
 *
 * Created on 17.05.2007
 * Created on 30.03.2014
 */
package net.finmath.montecarlo.interestrate.products;

import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;

import net.finmath.functions.AnalyticFormulas;
import net.finmath.marketdata.model.AnalyticModelFromCurvesAndVols;
import net.finmath.marketdata.model.curves.Curve;
import net.finmath.marketdata.model.curves.DiscountCurve;
import net.finmath.marketdata.model.curves.DiscountCurveFromForwardCurve;
import net.finmath.marketdata.model.curves.ForwardCurve;
import net.finmath.montecarlo.RandomVariableFromDoubleArray;
import net.finmath.montecarlo.interestrate.LIBORMarketModel;
import net.finmath.montecarlo.interestrate.TermStructureMonteCarloSimulationModel;
import net.finmath.montecarlo.model.ProcessModel;
import net.finmath.stochastic.RandomVariable;
import net.finmath.time.TimeDiscretization;
import net.finmath.time.TimeDiscretizationFromArray;

/**
 * This class implements an analytic swaption valuation formula under
 * a LIBOR market model. The algorithm implemented here is the
 * OIS discounting version of the algorithm described in
 * ISBN 0470047224 (see {@link net.finmath.montecarlo.interestrate.products.SwaptionSingleCurveAnalyticApproximation}).
 *
 * The approximation assumes that the forward rates (LIBOR) follow a
 * log normal model and that the model provides the integrated
 * instantaneous covariance of the log-forward rates.
 *
 * The getValue method calculates the approximated integrated instantaneous variance of the swap rate,
 * using the approximation of
 * \[
 * 	\frac{d log(S(t))}{d log(L(t))}
 * \]
 * according to Rebonato (1999).
 *
 * Since \( L \) is a vector, \( w \) is a gradient (vector). The class then approximates
 * the Black volatility of a swaption via
 * \[
 * 	\sigma_S^{2} T := \sum_{i,j} w_{i} \gamma_{i,j} w_{j}
 * \]
 * where \( (\gamma_{i,j})_{i,j = 1,...,m} \) is the covariance matrix of the forward rates.
 *
 * The valuation can be performed in terms of value or implied Black volatility.
 *
 * In this implementation we use the weights as specified by Rebonato (1998) and
 * not the one derived by Hull and White (1999/2000).
 *
 * @author Christian Fries
 * @date 17.05.2007.
 * @version 1.0
 */
public class SwaptionAnalyticApproximationRebonato extends AbstractTermStructureMonteCarloProduct implements net.finmath.modelling.products.Swaption {

	private final double      swaprate;
	private final double[]    swapTenor;       // Vector of swap tenor (period start and end dates). Start of first period is the option maturity.
	private final ValueUnit   valueUnit;

	/**
	 * Create an analytic swaption approximation product for
	 * log normal forward rate model.
	 *
	 * Note: It is implicitly assumed that swapTenor.getTime(0) is the exercise date (no forward starting).
	 *
	 * @param swaprate The strike swap rate of the swaption.
	 * @param swapTenor The swap tenor in doubles.
	 */
	public SwaptionAnalyticApproximationRebonato(final double swaprate, final TimeDiscretization swapTenor) {
		this(swaprate, swapTenor.getAsDoubleArray(), ValueUnit.VALUE);
	}

	/**
	 * Create an analytic swaption approximation product for
	 * log normal forward rate model.
	 *
	 * Note: It is implicitly assumed that swapTenor[0] is the exercise date (no forward starting).
	 *
	 * @param swaprate The strike swap rate of the swaption.
	 * @param swapTenor The swap tenor in doubles.
	 * @param valueUnit The unit of the quantity returned by the getValues method.
	 */
	public SwaptionAnalyticApproximationRebonato(final double swaprate, final double[] swapTenor, final ValueUnit valueUnit) {
		super();
		this.swaprate	= swaprate;
		this.swapTenor	= swapTenor;
		this.valueUnit	= valueUnit;
	}

	@Override
	public RandomVariable getValue(final double evaluationTime, final TermStructureMonteCarloSimulationModel model) {
		final ProcessModel modelBase = model.getModel();
		if(modelBase instanceof LIBORMarketModel) {
			return getValues(evaluationTime, model.getTimeDiscretization(), (LIBORMarketModel)modelBase);
		} else {
			throw new IllegalArgumentException("This product requires a simulation where the underlying model is of type LIBORMarketModel.");
		}
	}

	/**
	 * Calculates the approximated integrated instantaneous variance of the swap rate,
	 * using the approximation d log(S(t))/d log(L(t)) = d log(S(0))/d log(L(0)).
	 *
	 * @param evaluationTime Time at which the product is evaluated.
	 * @param timeDiscretization The time discretization used for integrating the covariance.
	 * @param model A model implementing the LIBORModelMonteCarloSimulationModel
	 * @return Depending on the value of value unit, the method returns either
	 * the approximated integrated instantaneous variance of the swap rate (ValueUnit.INTEGRATEDVARIANCE)
	 * or the value using the Black formula (ValueUnit.VALUE).
	 * @TODO make initial values an arg and use evaluation time.
	 */
	public RandomVariable getValues(final double evaluationTime, final TimeDiscretization timeDiscretization, final LIBORMarketModel model) {
		if(evaluationTime > 0) {
			throw new RuntimeException("Forward start evaluation currently not supported.");
		}

		final double swapStart    = swapTenor[0];
		final double swapEnd      = swapTenor[swapTenor.length-1];

		final int swapStartIndex  = model.getLiborPeriodIndex(swapStart);
		final int swapEndIndex    = model.getLiborPeriodIndex(swapEnd);
		final int optionMaturityIndex = model.getCovarianceModel().getTimeDiscretization().getTimeIndex(swapStart)-1;

		final Map<String, double[]>  logSwaprateDerivative  = getLogSwaprateDerivative(model.getLiborPeriodDiscretization(), model.getDiscountCurve(), model.getForwardRateCurve(), swapTenor);
		final double[]    swapCovarianceWeights  = logSwaprateDerivative.get("values");

		// Get the integrated libor covariance from the model
		final double[][]	integratedLIBORCovariance = model.getIntegratedLIBORCovariance(timeDiscretization)[optionMaturityIndex];

		// Calculate integrated swap rate covariance
		double integratedSwapRateVariance = 0.0;
		for(int componentIndex1 = swapStartIndex; componentIndex1 < swapEndIndex; componentIndex1++) {
			// Sum the libor cross terms (use symmetry)
			for(int componentIndex2 = componentIndex1+1; componentIndex2 < swapEndIndex; componentIndex2++) {
				integratedSwapRateVariance += 2.0 * swapCovarianceWeights[componentIndex1-swapStartIndex] * swapCovarianceWeights[componentIndex2-swapStartIndex] * integratedLIBORCovariance[componentIndex1][componentIndex2];
			}
			// Add diagonal term (libor variance term)
			integratedSwapRateVariance += swapCovarianceWeights[componentIndex1-swapStartIndex] * swapCovarianceWeights[componentIndex1-swapStartIndex] * integratedLIBORCovariance[componentIndex1][componentIndex1];
		}

		// Return integratedSwapRateVariance if requested
		if(valueUnit == ValueUnit.INTEGRATEDVARIANCELOGNORMAL || valueUnit == ValueUnit.INTEGRATEDVARIANCE) {
			return new RandomVariableFromDoubleArray(evaluationTime, integratedSwapRateVariance);
		}

		final double volatility		= Math.sqrt(integratedSwapRateVariance / swapStart);

		// Return integratedSwapRateVariance if requested
		if(valueUnit == ValueUnit.VOLATILITYLOGNORMAL || valueUnit == ValueUnit.VOLATILITY) {
			return new RandomVariableFromDoubleArray(evaluationTime, volatility);
		}

		// Use black formula for swaption to calculate the price
		final double parSwaprate		= net.finmath.marketdata.products.Swap.getForwardSwapRate(new TimeDiscretizationFromArray(swapTenor), new TimeDiscretizationFromArray(swapTenor), model.getForwardRateCurve(), model.getDiscountCurve());
		final double swapAnnuity      = net.finmath.marketdata.products.SwapAnnuity.getSwapAnnuity(new TimeDiscretizationFromArray(swapTenor), model.getDiscountCurve());

		final double optionMaturity	= swapStart;

		final double valueSwaption = AnalyticFormulas.blackModelSwaptionValue(parSwaprate, volatility, optionMaturity, swaprate, swapAnnuity);
		return new RandomVariableFromDoubleArray(evaluationTime, valueSwaption);
	}

	/**
	 * This function calculate the partial derivative <i>d log(S) / d log(L<sub>k</sub>)</i> for
	 * a given swap rate with respect to a vector of forward rates (on a given forward rate tenor).
	 *
	 * It also returns some useful other quantities like the corresponding discout factors and swap annuities.
	 *
	 * @param liborPeriodDiscretization The libor period discretization.
	 * @param discountCurve The discount curve. If this parameter is null, the discount curve will be calculated from the forward curve.
	 * @param forwardCurve The forward curve.
	 * @param swapTenor The swap tenor.
	 * @return A map containing the partial derivatives (key "value"), the discount factors (key "discountFactors") and the annuities (key "annuities") as vectors of double[] (indexed by forward rate tenor index starting at swap start)
	 */
	public static Map<String, double[]> getLogSwaprateDerivative(final TimeDiscretization liborPeriodDiscretization, DiscountCurve discountCurve, final ForwardCurve forwardCurve, final double[] swapTenor) {
		/*
		 * Small workaround for the case that the discount curve is not set. This part will be removed later.
		 */
		AnalyticModelFromCurvesAndVols model = null;
		if(discountCurve == null) {
			discountCurve	= new DiscountCurveFromForwardCurve(forwardCurve.getName());
			model					= new AnalyticModelFromCurvesAndVols(new Curve[] { forwardCurve, discountCurve });
		}

		final double swapStart    = swapTenor[0];
		final double swapEnd      = swapTenor[swapTenor.length-1];

		// Get the indices of the swap start and end on the forward rate tenor
		final int swapStartIndex  = liborPeriodDiscretization.getTimeIndex(swapStart);
		final int swapEndIndex    = liborPeriodDiscretization.getTimeIndex(swapEnd);

		// Precalculate forward rates and discount factors. Note: the swap contains swapEndIndex-swapStartIndex forward rates
		final double[] forwardRates       = new double[swapEndIndex-swapStartIndex+1];
		final double[] discountFactors    = new double[swapEndIndex-swapStartIndex+1];

		// Calculate discount factor at swap start
		discountFactors[0] = discountCurve.getDiscountFactor(model, swapStart);

		// Calculate discount factors for swap period ends (used for swap annuity)
		for(int liborPeriodIndex = swapStartIndex; liborPeriodIndex < swapEndIndex; liborPeriodIndex++) {
			final double libor = forwardCurve.getForward(null, liborPeriodDiscretization.getTime(liborPeriodIndex));

			forwardRates[liborPeriodIndex-swapStartIndex]       = libor;
			discountFactors[liborPeriodIndex-swapStartIndex+1]  = discountCurve.getDiscountFactor(model, liborPeriodDiscretization.getTime(liborPeriodIndex+1));
		}

		// Precalculate swap annuities
		final double[]    swapAnnuities   = new double[swapTenor.length-1];
		double      swapAnnuity     = 0.0;
		for(int swapPeriodIndex = swapTenor.length-2; swapPeriodIndex >= 0; swapPeriodIndex--) {
			final int periodEndIndex = liborPeriodDiscretization.getTimeIndex(swapTenor[swapPeriodIndex+1]);
			swapAnnuity += discountFactors[periodEndIndex-swapStartIndex] * (swapTenor[swapPeriodIndex+1]-swapTenor[swapPeriodIndex]);
			swapAnnuities[swapPeriodIndex] = swapAnnuity;
		}

		final int[] liborPeriodsInSwapPeriods = new int[swapTenor.length-1];
		Arrays.fill(liborPeriodsInSwapPeriods, 0);
		for(int liborPeriodIndex = swapStartIndex, swapPeriodIndex = 0; liborPeriodIndex < swapEndIndex; liborPeriodIndex++) {
			if(liborPeriodDiscretization.getTime(liborPeriodIndex) >= swapTenor[swapPeriodIndex+1]) {
				swapPeriodIndex++;
			}
			liborPeriodsInSwapPeriods[swapPeriodIndex]++;
		}

		// Precalculate weights: The formula is the one by Rebonato (note: this formula can be improved easily, we provide it rather for testing/illustration.
		final double[] swapCovarianceWeights = new double[swapEndIndex-swapStartIndex];

		for(int liborPeriodIndex = swapStartIndex, swapPeriodIndex = 0; liborPeriodIndex < swapEndIndex; liborPeriodIndex++) {
			if(liborPeriodDiscretization.getTime(liborPeriodIndex) >= swapTenor[swapPeriodIndex+1]) {
				swapPeriodIndex++;
			}

			final double swapAnnuityCurrent	= swapAnnuities[swapPeriodIndex];
			final double swapAnnuityNext		= swapPeriodIndex < swapAnnuities.length-1 ? swapAnnuities[swapPeriodIndex+1] : 0;

			swapCovarianceWeights[liborPeriodIndex-swapStartIndex] = (swapAnnuityCurrent-swapAnnuityNext)/swapAnnuity/ liborPeriodsInSwapPeriods[swapPeriodIndex];
		}

		// Return results
		final Map<String, double[]> results = new HashMap<>();
		results.put("values",			swapCovarianceWeights);
		results.put("discountFactors",	discountFactors);
		results.put("swapAnnuities",	swapAnnuities);

		return results;
	}
}