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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 23.03.2014
*/
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;
/**
* Implements the characteristic function of a Black Scholes model.
*
* @author Christian Fries
* @author Alessandro Gnoatto
* @version 1.0
*/
public class BlackScholesModel 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 volatility;
/**
* Create a Black Scholes model (characteristic function)
*
* @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 volatility \( \sigma \) the volatility level
*/
public BlackScholesModel(final LocalDate referenceDate, final double initialValue,
final DiscountCurve discountCurveForForwardRate, final DiscountCurve discountCurveForDiscountRate, final double volatility) {
super();
this.referenceDate = referenceDate;
this.initialValue = initialValue;
this.discountCurveForForwardRate = discountCurveForForwardRate;
riskFreeRate = Double.NaN;
this.discountCurveForDiscountRate = discountCurveForDiscountRate;
discountRate = Double.NaN;
this.volatility = volatility;
}
/**
* Create a Black Scholes model (characteristic function)
*
* @param initialValue \( S_{0} \) - spot - initial value of S
* @param riskFreeRate \( r^{\text{c}} \) - the risk free rate
* @param discountRate \( r^{\text{d}} \) - the discount rate
* @param volatility \( \sigma \) the volatility level
*/
public BlackScholesModel(final double initialValue, final double riskFreeRate, final double discountRate, final double volatility) {
super();
referenceDate = null;
this.initialValue = initialValue;
discountCurveForForwardRate = null;
this.riskFreeRate = riskFreeRate;
this.volatility = volatility;
discountCurveForDiscountRate = null;
this.discountRate = discountRate;
}
/**
* Create a Black Scholes model (characteristic function)
*
* @param initialValue \( S_{0} \) - spot - initial value of S
* @param riskFreeRate \( r^{\text{c}} \) - the risk free rate
* @param volatility \( \sigma \) the volatility level
*/
public BlackScholesModel(final double initialValue, final double riskFreeRate, final double volatility) {
this(initialValue, riskFreeRate, riskFreeRate, volatility);
}
@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);
return iargument
.multiply(
iargument
.multiply(0.5*volatility*volatility*time)
.add(Math.log(initialValue)-0.5*volatility*volatility*time-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
*/
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 volatility
*/
public double getVolatility() {
return volatility;
}
/* (non-Javadoc)
* @see java.lang.Object#toString()
*/
@Override
public String toString() {
return "BlackScholesModel [initialValue=" + initialValue + ", discountCurveForForwardRate="
+ discountCurveForForwardRate + ", riskFreeRate=" + riskFreeRate + ", discountCurveForDiscountRate="
+ discountCurveForDiscountRate + ", discountRate=" + discountRate + ", volatility=" + volatility + "]";
}
}