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finmath lib is a Mathematical Finance Library in Java.
It provides algorithms and methodologies related to mathematical finance.
/*
* (c) Copyright Christian P. Fries, Germany. Contact: [email protected].
*
* Created on 20.05.2005
*/
package net.finmath.marketdata.model.curves;
import java.io.Serializable;
import java.time.LocalDate;
import java.util.Arrays;
import net.finmath.marketdata.model.AnalyticModel;
/**
* Implementation of a discount factor curve given by a Nelson-Siegel-Svensson (NSS) parameterization.
* In the NSS parameterization the zero rate \( r(T) \) is given by
*
* \[ r(T) = \beta_0 + \beta_1 \frac{1-x_0}{T/\tau_0} + \beta_2 ( \frac{1-x_0}{T/\tau_0} - x_0) + \beta_3 ( \frac{1-x_1}{T/\tau_1} - x_1) \]
*
* where \( x_0 = \exp(-T/\tau_0) \) and \( x_1 = \exp(-T/\tau_1) \).
*
* The sub-family of curves with \( \beta_3 = 0 \) is called Nelson-Siegel parameterization.
*
* Note: This is a time-parameterized model. The finmath lib library uses an internal mapping from date to times \( t \).
* This mapping does not necessarily need to correspond with the curves understanding for the parameter \( T \).
* For that reason this class allows to re-scale the time parameter. Currently only a simple re-scaling factor is
* supported.
*
* The parameter T used in the parameterization is given by T = timeScaling * t, where t is the maturity as an ACT/365
* year fraction from the given reference date.
*
* @author Christian Fries
* @version 1.0
*/
public class DiscountCurveNelsonSiegelSvensson extends AbstractCurve implements Serializable, DiscountCurve {
private static final long serialVersionUID = 8024640795839972709L;
private final double timeScaling;
private final double[] parameter;
/**
* Create a discount curve using a Nelson-Siegel-Svensson parametrization.
*
* @param name The name of the curve (the curve can be referenced under this name, if added to an AnalyticModelFromCuvesAndVols.
* @param referenceDate The reference date of this curve, i.e. the date associated with t=0.
* @param parameter The Nelson-Siegel-Svensson parameters in the order \( ( \beta_0, \beta_1, \beta_2, \beta_3, \tau_0, \tau_1 ) \).
* @param timeScaling The time parameter argument rescaling. See {@link #getDiscountFactor(AnalyticModel, double)}.
*/
public DiscountCurveNelsonSiegelSvensson(final String name, final LocalDate referenceDate, final double[] parameter, final double timeScaling) {
super(name, referenceDate);
this.timeScaling = timeScaling;
this.parameter = parameter.clone();
}
@Override
public double getDiscountFactor(final double maturity)
{
return getDiscountFactor(null, maturity);
}
/**
* Return the discount factor within a given model context for a given maturity.
* @param model The model used as a context (not required for this class).
* @param maturity The maturity in terms of ACT/365 daycount form this curve reference date. Note that this parameter might get rescaled to a different time parameter.
* @see net.finmath.marketdata.model.curves.DiscountCurve#getDiscountFactor(net.finmath.marketdata.model.AnalyticModel, double)
*/
@Override
public double getDiscountFactor(final AnalyticModel model, double maturity)
{
// Change time scale
maturity *= timeScaling;
final double beta1 = parameter[0];
final double beta2 = parameter[1];
final double beta3 = parameter[2];
final double beta4 = parameter[3];
final double tau1 = parameter[4];
final double tau2 = parameter[5];
final double x1 = tau1 > 0 ? Math.exp(-maturity/tau1) : 0.0;
final double x2 = tau2 > 0 ? Math.exp(-maturity/tau2) : 0.0;
final double y1 = tau1 > 0 ? (maturity > 0.0 ? (1.0-x1)/maturity*tau1 : 1.0) : 0.0;
final double y2 = tau2 > 0 ? (maturity > 0.0 ? (1.0-x2)/maturity*tau2 : 1.0) : 0.0;
final double zeroRate = beta1 + beta2 * y1 + beta3 * (y1-x1) + beta4 * (y2-x2);
return Math.exp(- zeroRate * maturity);
}
@Override
public double getValue(final AnalyticModel model, final double time) {
return getDiscountFactor(model, time);
}
/**
* Returns the zero rate for a given maturity, i.e., -ln(df(T)) / T where T is the given maturity and df(T) is
* the discount factor at time $T$.
*
* @param maturity The given maturity.
* @return The zero rate.
*/
public double getZeroRate(final double maturity)
{
if(maturity == 0) {
return this.getZeroRate(1.0E-14);
}
return -Math.log(getDiscountFactor(null, maturity))/maturity;
}
/**
* Returns the zero rates for a given vector maturities.
*
* @param maturities The given maturities.
* @return The zero rates.
*/
public double[] getZeroRates(final double[] maturities)
{
final double[] values = new double[maturities.length];
for(int i=0; i