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finmath lib is a Mathematical Finance Library in Java.
It provides algorithms and methodologies related to mathematical finance.
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package net.finmath.singleswaprate.calibration;
import java.time.LocalDate;
import java.util.ArrayList;
import java.util.Map;
import java.util.Set;
import java.util.TreeMap;
import java.util.TreeSet;
import net.finmath.functions.AnalyticFormulas;
import net.finmath.marketdata.model.AnalyticModel;
import net.finmath.marketdata.model.volatilities.SwaptionDataLattice;
import net.finmath.marketdata.products.Swap;
import net.finmath.marketdata.products.SwapAnnuity;
import net.finmath.optimizer.LevenbergMarquardt;
import net.finmath.optimizer.SolverException;
import net.finmath.singleswaprate.data.DataTable;
import net.finmath.singleswaprate.data.DataTable.TableConvention;
import net.finmath.singleswaprate.data.DataTableExtrapolated;
import net.finmath.singleswaprate.data.DataTableLight;
import net.finmath.singleswaprate.data.DataTableLinear;
import net.finmath.singleswaprate.model.volatilities.SABRVolatilityCube;
import net.finmath.time.Schedule;
import net.finmath.time.SchedulePrototype;
/**
* Calibration of a {@link SABRVolatilityCube} by shifting increments in the market data of cash settled swaptions onto physically settled swaptions and calibrating a SABR model
* on the resulting smiles. The calibration happens per node and is thus much faster than a calibration of the whole cube at once.
*
* @author Christian Fries
* @author Roland Bachl
*
*/
public class SABRShiftedSmileCalibration {
private final LocalDate referenceDate;
private final AnalyticModel model;
private final SwaptionDataLattice cashPayerPremiums;
private final SwaptionDataLattice cashReceiverPremiums;
private final SwaptionDataLattice physicalPremiumsATM;
private final SchedulePrototype fixMetaSchedule;
private final SchedulePrototype floatMetaSchedule;
private final String discountCurveName;
private final String forwardCurveName;
private final double sabrDisplacement;
private final double sabrBeta;
private final double correlationDecay;
private final double iborOisDecorrelation;
private Map physicalVolatilities;
private Map cashPayerVolatilities;
private Map cashReceiverVolatilities;
private DataTableLight interpolationNodes;
private boolean useLinearInterpolation = true;
private DataTable swapRateTable;
private DataTable rhoTable;
private DataTable baseVolTable;
private DataTable volvolTable;
private int maxIterations = 500;
private int numberOfThreads = Runtime.getRuntime().availableProcessors();
/**
* Calibrate a cube via shifting cash settled swaption smiles onto physically settled swaption atm volatility.
* Using the default calibration parameters.
*
* @param name The name of the calibrated cube.
* @param referenceDate The reference date of the tables.
* @param cashPayerPremiums Lattice containing cash settled payer swaption premiums.
* @param cashReceiverPremiums Lattice containing cash settled receiver swaption premiums.
* @param physicalPremiumsATM Table containing physical settled swaption atm premiums.
* @param model The model for context.
* @param sabrDisplacement The displacement parameter the SABR smiles of the cube is supposed to have.
* @param sabrBeta The beta parameter the SABR smiles of the cubes are supposed to have.
* @param correlationDecay The correlation decay parameter the cube is supposed to have.
* @param iborOisDecorrelation The ibor ois decorrelation parameter the calibrated cube is sipposed to have.
*
* @return The calibrated cube.
*
* @throws SolverException Thrown when solvers fail to find suitable parameters.
*/
public static SABRVolatilityCube createSABRVolatilityCube(final String name, final LocalDate referenceDate,
final SwaptionDataLattice cashPayerPremiums, final SwaptionDataLattice cashReceiverPremiums, final SwaptionDataLattice physicalPremiumsATM,
final AnalyticModel model, final double sabrDisplacement, final double sabrBeta, final double correlationDecay, final double iborOisDecorrelation) throws SolverException {
final SABRShiftedSmileCalibration factory = new SABRShiftedSmileCalibration(referenceDate, cashPayerPremiums, cashReceiverPremiums, physicalPremiumsATM,
model, sabrDisplacement, sabrBeta, correlationDecay, iborOisDecorrelation);
return factory.build(name);
}
/**
* Return all data points as volatilities that serve as calibration targets. Points are sorted into maps according to their strike in moneyness.
*
* @param name The name of the tables. Will be amended by their strike in moneyness.
* @param referenceDate The reference date of the tables.
* @param cashPayerPremiums Lattice containing cash settled payer swaption premiums.
* @param cashReceiverPremiums Lattice containing cash settled receiver swaption premiums.
* @param physicalPremiumsATM Table containing physical settled swaption atm premiums.
* @param model The model for context.
* @return The set of maps containing market data volatility points.
*/
public static Map createVolatilityCubeLattice(final String name, final LocalDate referenceDate,
final SwaptionDataLattice cashPayerPremiums, final SwaptionDataLattice cashReceiverPremiums, final SwaptionDataLattice physicalPremiumsATM, final AnalyticModel model) {
final SABRShiftedSmileCalibration factory = new SABRShiftedSmileCalibration(referenceDate, cashPayerPremiums, cashReceiverPremiums, physicalPremiumsATM,
model, 0, 0, 0, 0);
try {
factory.build(name);
} catch (final SolverException e) {
// ignore this, lattice doesn't use calibrated cube
}
final TreeMap returnMap = new TreeMap<>();
for(final Map.Entry entry : factory.physicalVolatilities.entrySet()) {
returnMap.put(entry.getKey(), entry.getValue().clone());
}
return returnMap;
}
/**
* Create the calibrator to be able to modify calibration parameters before building the cube.
*
* @param referenceDate The reference date of the calibrated cube.
* @param cashPayerPremiums Lattice containing cash settled payer swaption premiums.
* @param cashReceiverPremiums Lattice containing cash settled receiver swaption premiums.
* @param physicalPremiumsATM Table containing physical settled swaption atm premiums.
* @param model The model providing context.
* @param sabrDisplacement The displacement parameter the SABR smiles of the cube is supposed to have.
* @param sabrBeta The beta parameter the SABR smiles of the cubes are supposed to have.
* @param correlationDecay The correlation decay parameter the cube is supposed to have.
* @param iborOisDecorrelation The ibor ois decorrelation parameter the calibrated cube is supposed to have.
*/
public SABRShiftedSmileCalibration(final LocalDate referenceDate, final SwaptionDataLattice cashPayerPremiums, final SwaptionDataLattice cashReceiverPremiums,
final SwaptionDataLattice physicalPremiumsATM, final AnalyticModel model,
final double sabrDisplacement, final double sabrBeta, final double correlationDecay, final double iborOisDecorrelation) {
super();
this.referenceDate = referenceDate;
this.physicalPremiumsATM = physicalPremiumsATM;
this.cashPayerPremiums = cashPayerPremiums;
this.cashReceiverPremiums = cashReceiverPremiums;
this.model = model;
this.sabrDisplacement = sabrDisplacement;
this.sabrBeta = sabrBeta;
this.correlationDecay = correlationDecay;
this.iborOisDecorrelation = iborOisDecorrelation;
fixMetaSchedule = cashPayerPremiums.getFixMetaSchedule();
floatMetaSchedule = cashPayerPremiums.getFloatMetaSchedule();
discountCurveName = cashPayerPremiums.getDiscountCurveName();
forwardCurveName = cashPayerPremiums.getForwardCurveName();
}
/**
* Perform the calibrations and build the cube.
*
* @param name The name of the cube.
* @return The calibrated cube.
*
* @throws SolverException Thrown when solvers fail to find suitable parameters.
*/
public SABRVolatilityCube build(final String name) throws SolverException {
findInterpolationNodes();
makeSwapRateTable();
findPayerVolatilities();
findReceiverVolatilities();
makePhysicalVolatilities();
calibrateSmilesOnNodes();
return new SABRVolatilityCube(name, referenceDate, swapRateTable, sabrDisplacement, sabrBeta, rhoTable, baseVolTable, volvolTable,
correlationDecay, iborOisDecorrelation);
}
/**
* Calibrate the SABR smiles on each node.
*
* @throws SolverException Thrown when solvers fail to find suitable parameters.
*/
private void calibrateSmilesOnNodes() throws SolverException {
// lists for all parameter maps
final ArrayList maturities = new ArrayList<>();
final ArrayList terminations = new ArrayList<>();
final ArrayList sabrRhos = new ArrayList<>();
final ArrayList sabrBaseVols = new ArrayList<>();
final ArrayList sabrVolvols = new ArrayList<>();
// calibrate a SABR smile on each node of the grid
double[] initialParameters = new double[]{ 0.01, 0.15, 0.3 }; // baseVol, volVol, rho
final int[] maturityArray = new int[interpolationNodes.getMaturities().size()];
final int[] terminationArray = new int[interpolationNodes.getTerminations().size()];
// going through nodes in reverse, because we want to use results from longer tenors for calibration of shorter ones
int index = maturityArray.length-1;
for(final int maturity : interpolationNodes.getMaturities()) {
maturityArray[index--] = maturity;
}
index = terminationArray.length-1;
for(final int termination : interpolationNodes.getTerminations()) {
terminationArray[index--] = termination;
}
for(final int maturity : maturityArray) {
for(final int termination : terminationArray) {
final double parSwapRate = swapRateTable.getValue(maturity, termination);
final double sabrMaturity = floatMetaSchedule.generateSchedule(referenceDate, referenceDate.plusMonths(maturity),
referenceDate.plusMonths(maturity+termination)).getFixing(0);
// gather smile points
int count = 0;
for(final int moneyness : physicalVolatilities.keySet()) {
if(physicalVolatilities.get(moneyness).containsEntryFor(maturity, termination)) {
count++;
}
}
final double[] marketStrikes = new double[count];
final double[] marketVolatilities = new double[count];
index = 0;
for(final int moneyness : physicalVolatilities.keySet()) {
if(physicalVolatilities.get(moneyness).containsEntryFor(maturity, termination)) {
marketStrikes[index] = parSwapRate + moneyness /10000.0;
marketVolatilities[index++] = physicalVolatilities.get(moneyness).getValue(maturity, termination);
}
}
// calibrate SABR
final LevenbergMarquardt optimizer = new LevenbergMarquardt(
initialParameters,
marketVolatilities,
maxIterations,
numberOfThreads
) {
private static final long serialVersionUID = -7551690451877166912L;
@Override
public void setValues(final double[] parameters, final double[] values) {
// making sure that volatility stays above 0 and rho between -1 and 1.
parameters[0] = Math.max(parameters[0], 0);
parameters[1] = Math.max(parameters[1], 0);
parameters[2] = Math.max(Math.min(parameters[2], 1), -1);
for(int i = 0; i < marketStrikes.length; i++) {
values[i] = AnalyticFormulas.sabrBerestyckiNormalVolatilityApproximation(parameters[0] /* alpha */, sabrBeta /* beta */,
parameters[2] /* rho */, parameters[1] /* nu */, sabrDisplacement /* displacement */,
parSwapRate, marketStrikes[i], sabrMaturity);
}
}
};
optimizer.run();
// System.out.println("Optimizer for node "+maturity+"x"+termination+" finished after " +optimizer.getIterations() +
// " iterations with mean error " + optimizer.getRootMeanSquaredError());
final double[] parameters = optimizer.getBestFitParameters();
// sort calibrated parameters into lists
maturities.add(maturity);
terminations.add(termination);
sabrBaseVols.add(parameters[0]);
sabrVolvols.add(parameters[1]);
sabrRhos.add(parameters[2]);
initialParameters = parameters;
}
}
if(useLinearInterpolation) {
baseVolTable = new DataTableLinear("MarketBaseVolatilityTable", TableConvention.MONTHS, referenceDate, floatMetaSchedule, maturities,
terminations, sabrBaseVols);
volvolTable = new DataTableLinear("MarketVolVolTable", TableConvention.MONTHS, referenceDate, floatMetaSchedule, maturities, terminations,
sabrVolvols);
rhoTable = new DataTableLinear("MarketRhoTable", TableConvention.MONTHS, referenceDate, floatMetaSchedule, maturities, terminations, sabrRhos);
} else {
baseVolTable = new DataTableExtrapolated("MarketBaseVolatilityTable", TableConvention.MONTHS, referenceDate, floatMetaSchedule, maturities,
terminations, sabrBaseVols);
volvolTable = new DataTableExtrapolated("MarketVolVolTable", TableConvention.MONTHS, referenceDate, floatMetaSchedule, maturities, terminations,
sabrVolvols);
rhoTable = new DataTableExtrapolated("MarketRhoTable", TableConvention.MONTHS, referenceDate, floatMetaSchedule, maturities, terminations, sabrRhos);
}
}
/**
* Identify the nodes on which to calibrate.
*/
private void findInterpolationNodes() {
final ArrayList nodeMaturities = new ArrayList<>();
final ArrayList nodeTerminations = new ArrayList<>();
final ArrayList nodeCardinalities = new ArrayList<>();
final Set payerStrikes = new TreeSet<>(cashPayerPremiums.getGridNodesPerMoneyness().keySet());
payerStrikes.remove(0);
final Set receiverStrikes = new TreeSet<>(cashReceiverPremiums.getGridNodesPerMoneyness().keySet());
receiverStrikes.remove(0);
for(final int maturity : physicalPremiumsATM.getMaturities()) {
for(final int termination : physicalPremiumsATM.getTenors(0, maturity)) {
int count = 1;
for(final int strike : payerStrikes) {
if(cashPayerPremiums.containsEntryFor(maturity, termination, strike)) {
count++;
}
}
for(final int strike : receiverStrikes) {
if(cashReceiverPremiums.containsEntryFor(maturity, termination, strike)) {
count++;
}
}
//only consider if there are more than a single point for a given node
if(count > 1) {
nodeMaturities.add(maturity);
nodeTerminations.add(termination);
nodeCardinalities.add((double) count);
}
}
}
interpolationNodes = new DataTableLight("NodesWithCardinality", TableConvention.MONTHS, nodeMaturities, nodeTerminations,
nodeCardinalities);
// fix holes (as interpolation needs a regular grid)
if(interpolationNodes.size() != interpolationNodes.getMaturities().size() * interpolationNodes.getTerminations().size()) {
for(final int maturity : interpolationNodes.getMaturities()) {
for(final int termination : interpolationNodes.getTerminations()) {
if(! interpolationNodes.containsEntryFor(maturity, termination)) {
interpolationNodes = interpolationNodes.addPoint(maturity, termination, 1);
}
}
}
}
}
/**
* Make physical volatility smiles, by shifting cash volatility smiles to physical atm level.
*/
private void makePhysicalVolatilities() {
// atm base
final int[] maturitiesArray = new int[interpolationNodes.size()];
final int[] terminationsArray = new int[interpolationNodes.size()];
final double[] volatilitiesArray = new double[interpolationNodes.size()];
int index = 0;
for(final int maturity : interpolationNodes.getMaturities()) {
for(final int termination : interpolationNodes.getTerminationsForMaturity(maturity)) {
maturitiesArray[index] = maturity;
terminationsArray[index] = termination;
final LocalDate maturityDate = referenceDate.plusMonths(maturity);
final LocalDate terminationDate = maturityDate.plusMonths(termination);
final Schedule fixSchedule = fixMetaSchedule.generateSchedule(referenceDate, maturityDate, terminationDate);
final double annuity = SwapAnnuity.getSwapAnnuity(fixSchedule.getFixing(0), fixSchedule, model.getDiscountCurve(discountCurveName), model);
final double swapRate = swapRateTable.getValue(maturity, termination);
volatilitiesArray[index++] = AnalyticFormulas.bachelierOptionImpliedVolatility(swapRate, fixSchedule.getFixing(0), swapRate, annuity,
physicalPremiumsATM.getValue(maturity, termination, 0));
}
}
final DataTableLight physicalATMTable = new DataTableLight("VolatilitiesPhysicalATM", TableConvention.MONTHS, maturitiesArray, terminationsArray,
volatilitiesArray);
physicalVolatilities = new TreeMap<>();
physicalVolatilities.put(0, physicalATMTable);
final DataTableLight payerATMTable = cashPayerVolatilities.get(0);
final DataTableLight receiverATMTable = cashReceiverVolatilities.get(0);
// imitate physical smile via cash smiles
final Set strikes = new TreeSet<>(cashPayerVolatilities.keySet());
strikes.addAll(cashReceiverVolatilities.keySet());
strikes.remove(0);
for(final int strike : strikes) {
//lists for bulk-initialization of tables
final ArrayList maturitiesPositive = new ArrayList<>();
final ArrayList terminationsPositive = new ArrayList<>();
final ArrayList physicalVolatilitiesPositive = new ArrayList<>();
final ArrayList maturitiesNegative = new ArrayList<>();
final ArrayList terminationsNegative = new ArrayList<>();
final ArrayList physicalVolatilitiesNegative = new ArrayList<>();
// shifting surface by shifting each individual point
for(final int maturity : interpolationNodes.getMaturities()) {
for(final int termination : interpolationNodes.getTerminationsForMaturity(maturity)) {
final double physicalATM = physicalATMTable.getValue(maturity, termination);
//shifting positive wing like payer
if(cashPayerVolatilities.containsKey(strike) && cashPayerVolatilities.get(strike).containsEntryFor(maturity, termination)) {
final double payerATM = payerATMTable.getValue(maturity, termination);
final double payerSmile = cashPayerVolatilities.get(strike).getValue(maturity, termination);
maturitiesPositive.add(maturity);
terminationsPositive.add(termination);
physicalVolatilitiesPositive.add(payerSmile - payerATM + physicalATM);
}
//shifting negative wing like receiver
if(cashReceiverVolatilities.containsKey(strike) && cashReceiverVolatilities.get(strike).containsEntryFor(maturity, termination)) {
final double receiverATM = receiverATMTable.getValue(maturity, termination);
final double receiverSmile = cashReceiverVolatilities.get(strike).getValue(maturity, termination);
maturitiesNegative.add(maturity);
terminationsNegative.add(termination);
physicalVolatilitiesNegative.add(receiverSmile - receiverATM + physicalATM);
}
}
}
final DataTableLight physicalPositiveSmileTable = new DataTableLight("VolatilitiesPhysical" + strike, TableConvention.MONTHS,
maturitiesPositive, terminationsPositive, physicalVolatilitiesPositive);
final DataTableLight physicalNegativeSmileTable = new DataTableLight("VolatilitiesPhysical" + -strike, TableConvention.MONTHS,
maturitiesNegative, terminationsNegative, physicalVolatilitiesNegative);
physicalVolatilities.put( strike, physicalPositiveSmileTable);
physicalVolatilities.put(-strike, physicalNegativeSmileTable);
}
}
/**
* Construct the volatility (half-) smile of cash settled payer swaptions.
*/
private void findPayerVolatilities() {
//convert to volatilities
cashPayerVolatilities = new TreeMap<>();
for(final int moneyness : cashPayerPremiums.getGridNodesPerMoneyness().keySet()) {
final ArrayList maturities = new ArrayList<>();
final ArrayList terminations = new ArrayList<>();
final ArrayList values = new ArrayList<>();
for(final int maturity : interpolationNodes.getMaturities()) {
for(final int termination : interpolationNodes.getTerminationsForMaturity(maturity)) {
if(cashPayerPremiums.containsEntryFor(maturity, termination, moneyness)){
final LocalDate maturityDate = referenceDate.plusMonths(maturity);
final LocalDate terminationDate = maturityDate.plusMonths(termination);
final Schedule fixSchedule = fixMetaSchedule.generateSchedule(referenceDate, maturityDate, terminationDate);
final double swapRate = swapRateTable.getValue(maturity, termination);
final double cashAnnuity = cashFunction(swapRate, fixSchedule);
maturities.add(maturity);
terminations.add(termination);
values.add(AnalyticFormulas.bachelierOptionImpliedVolatility(swapRate, fixSchedule.getFixing(0), swapRate + moneyness /10000.0,
cashAnnuity, cashPayerPremiums.getValue(maturity, termination, moneyness)));
}
}
}
final DataTableLight volatilityTable = new DataTableLight("VolatilitiesPayer"+moneyness, TableConvention.MONTHS, maturities, terminations, values);
cashPayerVolatilities.put(moneyness, volatilityTable);
}
}
/**
* Construct the volatility (half-) smile of cash settled receiver swaptions.
*/
private void findReceiverVolatilities() {
//convert to volatilities
cashReceiverVolatilities = new TreeMap<>();
for(final int moneyness : cashReceiverPremiums.getGridNodesPerMoneyness().keySet()) {
final ArrayList maturities = new ArrayList<>();
final ArrayList terminations = new ArrayList<>();
final ArrayList values = new ArrayList<>();
for(final int maturity : interpolationNodes.getMaturities()) {
for(final int termination : interpolationNodes.getTerminationsForMaturity(maturity)) {
if(cashReceiverPremiums.containsEntryFor(maturity, termination, moneyness)){
final LocalDate maturityDate = referenceDate.plusMonths(maturity);
final LocalDate terminationDate = maturityDate.plusMonths(termination);
final Schedule fixSchedule = fixMetaSchedule.generateSchedule(referenceDate, maturityDate, terminationDate);
final double swapRate = swapRateTable.getValue(maturity, termination);
final double cashAnnuity = cashFunction(swapRate, fixSchedule);
maturities.add(maturity);
terminations.add(termination);
values.add(AnalyticFormulas.bachelierOptionImpliedVolatility(swapRate, fixSchedule.getFixing(0), swapRate-moneyness/10000.0,
cashAnnuity, cashReceiverPremiums.getValue(maturity, termination, moneyness) + moneyness/10000.0 * cashAnnuity));
}
}
}
final DataTableLight volatilityTable = new DataTableLight("VolatilitiesReceiver"+moneyness, TableConvention.MONTHS, maturities, terminations, values);
cashReceiverVolatilities.put(moneyness, volatilityTable);
}
}
/**
* Build the table of swap rates as underlyings for the SABR smiles.
*/
private void makeSwapRateTable() {
final int[] maturitiesArray = new int[interpolationNodes.size()];
final int[] terminationsArray = new int[interpolationNodes.size()];
final double[] swapRateArray = new double[interpolationNodes.size()];
int index = 0;
for(final int maturity : interpolationNodes.getMaturities()) {
for(final int termination : interpolationNodes.getTerminationsForMaturity(maturity)) {
maturitiesArray[index] = maturity;
terminationsArray[index] = termination;
final LocalDate maturityDate = referenceDate.plusMonths(maturity);
final LocalDate terminationDate = maturityDate.plusMonths(termination);
final Schedule floatSchedule = floatMetaSchedule.generateSchedule(referenceDate, maturityDate, terminationDate);
final Schedule fixSchedule = fixMetaSchedule.generateSchedule(referenceDate, maturityDate, terminationDate);
final double swapRate = Swap.getForwardSwapRate(fixSchedule, floatSchedule, model.getForwardCurve(forwardCurveName), model);
swapRateArray[index++] = swapRate;
}
}
if(useLinearInterpolation) {
swapRateTable = new DataTableLinear("MarketParSwapRates", TableConvention.MONTHS, referenceDate, floatMetaSchedule, maturitiesArray,
terminationsArray, swapRateArray);
} else {
swapRateTable = new DataTableExtrapolated("MarketParSwapRates", TableConvention.MONTHS, referenceDate, floatMetaSchedule, maturitiesArray,
terminationsArray, swapRateArray);
}
}
/**
* Set the parameters for calibration.
*
* @param maxIterations The maximum number of iterations done during calibration.
* @param numberOfThreads The number of processor threads to be used.
*/
public void setCalibrationParameters( final int maxIterations, final int numberOfThreads) {
this.maxIterations = maxIterations;
this.numberOfThreads = numberOfThreads;
}
/**
* @return The maximum number of iterations of the optimizer.
*/
public int getMaxIterations() {
return maxIterations;
}
/**
* @return The number of threads the optimizer is allowed to use.
*/
public int getNumberOfThreads() {
return numberOfThreads;
}
/**
* @return True if tables holding SABR parameters use linear interpolation, false if piecewise cubic spline.
*/
public boolean isUseLinearInterpolation() {
return useLinearInterpolation;
}
/**
* @param useLinearInterpolation Set whether the interpolation of SABR parameters should be linear as opposed to piecewise cubic spline.
*/
public void setUseLinearInterpolation(final boolean useLinearInterpolation) {
this.useLinearInterpolation = useLinearInterpolation;
}
/**
* Cash function of cash settled swaptions for equidistant tenors.
*
* @param swapRate The swap rate.
* @param schedule The schedule.
* @return The result of the cash function.
*/
private static double cashFunction(final double swapRate, final Schedule schedule) {
final int numberOfPeriods = schedule.getNumberOfPeriods();
double periodLength = 0.0;
for(int index = 0; index < numberOfPeriods; index++) {
periodLength += schedule.getPeriodLength(index);
}
periodLength /= schedule.getNumberOfPeriods();
if(swapRate == 0.0) {
return numberOfPeriods * periodLength;
} else {
return (1 - Math.pow(1 + periodLength * swapRate, - numberOfPeriods)) / swapRate;
}
}
}