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finmath lib is a Mathematical Finance Library in Java.
It provides algorithms and methodologies related to mathematical finance.
package net.finmath.fouriermethod.models;
import java.time.LocalDate;
import org.apache.commons.math3.complex.Complex;
import net.finmath.fouriermethod.CharacteristicFunction;
import net.finmath.marketdata.model.curves.DiscountCurve;
import net.finmath.time.FloatingpointDate;
/**
* Implements the characteristic function of a Variance Gamma model.
*
* The Variange Gamma model is constructed from a subordinated Brownian motion, where the subordinator is given
* by a Gamma process.
*
* @author Alessandro Gnoatto
* @version 1.0
*/
public class VarianceGammaModel implements CharacteristicFunctionModel {
private final LocalDate referenceDate;
private final double initialValue;
private final DiscountCurve discountCurveForForwardRate;
private final double riskFreeRate; // Constant rate, used if discountCurveForForwardRate is null
private final DiscountCurve discountCurveForDiscountRate;
private final double discountRate; // Constant rate, used if discountCurveForForwardRate is null
private final double sigma;
private final double theta;
private final double nu;
/**
* Construct a Variance Gamma model with discount curves for the forward price (i.e. repo rate minus dividend yield) and for discounting.
*
* @param referenceDate The date representing the time t = 0. All other double times are following {@link net.finmath.time.FloatingpointDate}.
* @param initialValue \( S_{0} \) - spot - initial value of S
* @param discountCurveForForwardRate The curve specifying \( t \mapsto exp(- r^{\text{c}}(t) \cdot t) \) - with \( r^{\text{c}}(t) \) the risk free rate
* @param discountCurveForDiscountRate The curve specifying \( t \mapsto exp(- r^{\text{d}}(t) \cdot t) \) - with \( r^{\text{d}}(t) \) the discount rate
* @param sigma The parameter \( \sigma \)
* @param theta The parameter \( \theta \)
* @param nu The parameter \( \nu \)
*/
public VarianceGammaModel(final LocalDate referenceDate, final double initialValue, final DiscountCurve discountCurveForForwardRate,
final DiscountCurve discountCurveForDiscountRate, final double sigma, final double theta, final double nu) {
super();
this.referenceDate = referenceDate;
this.initialValue = initialValue;
this.discountCurveForForwardRate = discountCurveForForwardRate;
riskFreeRate = Double.NaN;
this.discountCurveForDiscountRate = discountCurveForDiscountRate;
discountRate = Double.NaN;
this.sigma = sigma;
this.theta = theta;
this.nu = nu;
}
/**
* Construct a Variance Gamma model with constant rates for the forward price (i.e. repo rate minus dividend yield) and for the discount curve.
*
* @param initialValue \( S_{0} \) - spot - initial value of S
* @param riskFreeRate The constant risk free rate for the drift (repo rate of the underlying).
* @param sigma The parameter \( \sigma \)
* @param theta The parameter \( \theta \)
* @param nu The parameter \( \nu \)
* @param discountRate The constant rate used for discounting.
*/
public VarianceGammaModel(final double initialValue, final double riskFreeRate, final double discountRate, final double sigma, final double theta,
final double nu) {
super();
referenceDate = null;
this.initialValue = initialValue;
discountCurveForForwardRate = null;
this.riskFreeRate = riskFreeRate;
discountCurveForDiscountRate = null;
this.discountRate = discountRate;
this.sigma = sigma;
this.theta = theta;
this.nu = nu;
}
@Override
public CharacteristicFunction apply(final double time) {
final double logDiscountFactorForForward = this.getLogDiscountFactorForForward(time);
final double logDiscountFactorForDiscounting = this.getLogDiscountFactorForDiscounting(time);
return new CharacteristicFunction() {
@Override
public Complex apply(final Complex argument) {
final Complex iargument = argument.multiply(Complex.I);
final Complex denominator = ((Complex.ONE).subtract(iargument.multiply(theta*nu))).add(argument.multiply(argument).multiply(0.5*sigma*sigma*nu));
final Complex firstLevyExponent = (((Complex.ONE).divide(denominator)).log()).multiply(time/nu);
final Complex compensator = iargument.multiply(time/nu * Math.log(1/(1.0-theta*nu-0.5*sigma*sigma*nu)));
return (firstLevyExponent.subtract(compensator)
.add(iargument.multiply(Math.log(initialValue)-logDiscountFactorForForward))
.add(logDiscountFactorForDiscounting))
.exp();
}
};
}
/**
* Small helper to calculate rate off the curve or use constant.
*
* @param time Maturity.
* @return The log of the discount factor, i.e., - rate * time.
*/
private double getLogDiscountFactorForForward(final double time) {
return discountCurveForForwardRate == null ? -riskFreeRate * time : Math.log(discountCurveForForwardRate.getDiscountFactor(null, time));
}
/**
* Small helper to calculate rate off the curve or use constant.
*
* @param time Maturity.
* @return The log of the discount factor, i.e., - rate * time.
*/
private double getLogDiscountFactorForDiscounting(final double time) {
return discountCurveForDiscountRate == null ? -discountRate * time : Math.log(discountCurveForDiscountRate.getDiscountFactor(null, time));
}
/**
* @return the referenceDate: The date corresponding to t = 0 (when dealing with {@link FloatingpointDate}s.
*/
public LocalDate getReferenceDate() {
return referenceDate;
}
/**
* @return the initialValue
*/
public double getInitialValue() {
return initialValue;
}
/**
* @return the discountCurveForForwardRate
*/
public DiscountCurve getDiscountCurveForForwardRate() {
return discountCurveForForwardRate;
}
/**
* @return the riskFreeRate
*/
public double getRiskFreeRate() {
return riskFreeRate;
}
/**
* @return the discountCurveForDiscountRate
*/
public DiscountCurve getDiscountCurveForDiscountRate() {
return discountCurveForDiscountRate;
}
/**
* @return the discountRate
*/
public double getDiscountRate() {
return discountRate;
}
/**
* @return the sigma
*/
public double getSigma() {
return sigma;
}
/**
* @return the theta
*/
public double getTheta() {
return theta;
}
/**
* @return the nu
*/
public double getNu() {
return nu;
}
@Override
public String toString() {
return "VarianceGammaModel [referenceDate=" + referenceDate + ", initialValue=" + initialValue
+ ", discountCurveForForwardRate=" + discountCurveForForwardRate + ", riskFreeRate=" + riskFreeRate
+ ", discountCurveForDiscountRate=" + discountCurveForDiscountRate + ", discountRate=" + discountRate
+ ", sigma=" + sigma + ", theta=" + theta + ", nu=" + nu + "]";
}
}