net.finmath.marketdata.model.volatilities.CapletVolatilitiesParametric Maven / Gradle / Ivy
Go to download
Show more of this group Show more artifacts with this name
Show all versions of finmath-lib Show documentation
Show all versions of finmath-lib Show documentation
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 30.08.2014
*/
package net.finmath.marketdata.model.volatilities;
import java.time.LocalDate;
import net.finmath.marketdata.model.AnalyticModelInterface;
import net.finmath.marketdata.model.curves.DiscountCurveInterface;
import net.finmath.marketdata.model.curves.ForwardCurveInterface;
/**
* A parametric caplet volatility surface created form the four parameter model
* for the instantaneous forward rate lognormal volatility given by
* \( \sigma(t) = (a + b t) \exp(- c t) + d \).
*
* In other words, the Black volatility for maturity T is given by
* \[ \sqrt{ \frac{1}{T} \int_0^T ((a + b t) \exp(- c t) + d)^2 dt } \].
*
* Note: quoting convention of the functional form is LOGNORMAL, but container may
* provide data in other conventions.
*
* @author Christian Fries
*/
public class CapletVolatilitiesParametric extends AbstractVolatilitySurfaceParametric {
private final double timeScaling;
private final double a,b,c,d;
/**
* Create a model with parameters a,b,c,d defining a lognormal volatility surface.
*
* @param name The name of this volatility surface.
* @param referenceDate The reference date for this volatility surface, i.e., the date which defined t=0.
* @param forwardCurve The underlying forward curve.
* @param discountCurve The associated discount curve.
* @param a The parameter a
* @param b The parameter b
* @param c The parameter c
* @param d The parameter d
* @param timeScaling A scaling factor applied to t when converting from global double time to the parametric function argument t.
* @param quotingConvention The quoting convention reflected by the parametetric form (e.g. lognormal or normal).
*/
public CapletVolatilitiesParametric(String name, LocalDate referenceDate,
ForwardCurveInterface forwardCurve,
DiscountCurveInterface discountCurve,
double a, double b, double c, double d, double timeScaling, QuotingConvention quotingConvention) {
super(name, referenceDate);
this.forwardCurve = forwardCurve;
this.discountCurve = discountCurve;
this.timeScaling = timeScaling;
this.a = a;
this.b = b;
this.c = c;
this.d = d;
this.quotingConvention = quotingConvention;
}
/**
* Create a model with parameters a,b,c,d defining a lognormal volatility surface.
*
* @param name The name of this volatility surface.
* @param referenceDate The reference date for this volatility surface, i.e., the date which defined t=0.
* @param forwardCurve The underlying forward curve.
* @param discountCurve The associated discount curve.
* @param a The parameter a
* @param b The parameter b
* @param c The parameter c
* @param d The parameter d
* @param timeScaling A scaling factor applied to t when converting from global double time to the parametric function argument t.
*/
public CapletVolatilitiesParametric(String name, LocalDate referenceDate,
ForwardCurveInterface forwardCurve,
DiscountCurveInterface discountCurve,
double a, double b, double c, double d, double timeScaling) {
super(name, referenceDate);
this.forwardCurve = forwardCurve;
this.discountCurve = discountCurve;
this.timeScaling = timeScaling;
this.a = a;
this.b = b;
this.c = c;
this.d = d;
this.quotingConvention = QuotingConvention.VOLATILITYLOGNORMAL;
}
/**
* Create a model with parameters a,b,c,d.
*
* @param name The name of this volatility surface.
* @param referenceDate The reference date for this volatility surface, i.e., the date which defined t=0.
* @param a The parameter a
* @param b The parameter b
* @param c The parameter c
* @param d The parameter d
* @param timeScaling A scaling factor applied to t when converting from global double time to the parametric function argument t.
*/
public CapletVolatilitiesParametric(String name, LocalDate referenceDate,
double a, double b, double c, double d, double timeScaling) {
this(name, referenceDate, null, null, a, b, c, d, timeScaling);
}
/**
* Create a model with parameters a,b,c,d.
*
* @param name The name of this volatility surface.
* @param referenceDate The reference date for this volatility surface, i.e., the date which defined t=0.
* @param a The parameter a
* @param b The parameter b
* @param c The parameter c
* @param d The parameter d
*/
public CapletVolatilitiesParametric(String name, LocalDate referenceDate, double a, double b, double c, double d) {
this(name, referenceDate, a, b, c, d, 1.0);
}
/* (non-Javadoc)
* @see net.finmath.marketdata.model.volatilities.VolatilitySurfaceInterface#getValue(double, double, net.finmath.marketdata.model.volatilities.VolatilitySurfaceInterface.QuotingConvention)
*/
@Override
public double getValue(double maturity, double strike, QuotingConvention quotingConvention) {
return getValue(null, maturity, strike, quotingConvention);
}
/* (non-Javadoc)
* @see net.finmath.marketdata.model.volatilities.VolatilitySurfaceInterface#getValue(net.finmath.marketdata.model.AnalyticModelInterface, double, double, net.finmath.marketdata.model.volatilities.VolatilitySurfaceInterface.QuotingConvention)
*/
@Override
public double getValue(AnalyticModelInterface model, double maturity, double strike, QuotingConvention quotingConvention) {
if(maturity <= 0) return 0;
double T = maturity * timeScaling;
/*
* Integral of the square of the instantaneous volatility function
* ((a + b * T) * Math.exp(- c * T) + d);
*/
double integratedVariance;
if(c != 0) {
/*
* http://www.wolframalpha.com/input/?i=integrate+%28%28a+%2B+b+*+t%29+*+exp%28-+c+*+t%29+%2B+d%29%5E2+from+0+to+T
* integral_0^T ((a+b t) exp(-(c t))+d)^2 dt = 1/4 ((e^(-2 c T) (-2 a^2 c^2-2 a b c (2 c T+1)+b^2 (-(2 c T (c T+1)+1))))/c^3+(2 a^2 c^2+2 a b c+b^2)/c^3-(8 d e^(-c T) (a c+b c T+b))/c^2+(8 d (a c+b))/c^2+4 d^2 T)
*/
integratedVariance = a*a*T*((1-Math.exp(-2*c*T))/(2*c*T))
+ a*b*T*T*(((1 - Math.exp(-2*c*T))/(2*c*T) - Math.exp(-2*c*T))/(c*T))
+ 2*a*d*T*((1-Math.exp(-c*T))/(c*T))
+ b*b*T*T*T*(((((1-Math.exp(-2*c*T))/(2*c*T)-Math.exp(-2*c*T))/(T*c)-Math.exp(-2*c*T)))/(2*c*T))
+ 2*b*d*T*T*(((1-Math.exp(-c*T))-T*c*Math.exp(-c*T))/(c*c*T*T))
+ d*d*T;
}
else {
/*
* http://www.wolframalpha.com/input/?i=expand+%28integrate+%28%28a+%2B+b+*+t%29+%2B+d%29%5E2+from+0+to+T%29
*/
integratedVariance = a*a*T + a*b*T*T + 2*a*d*T + (b*b*T*T*T)/3.0 + b*d*T*T + d*d*T;
}
double value = Math.sqrt(integratedVariance/maturity);
return convertFromTo(model, maturity, strike, value, this.quotingConvention, quotingConvention);
}
@Override
public double[] getParameter() {
double[] parameter = new double[4];
parameter[0] = a;
parameter[1] = b;
parameter[2] = c;
parameter[3] = d;
return parameter;
}
@Override
public void setParameter(double[] parameter) {
throw new UnsupportedOperationException("This class is immutable.");
}
@Override
public AbstractVolatilitySurfaceParametric getCloneForParameter(double[] value) throws CloneNotSupportedException {
return new CapletVolatilitiesParametric(getName(), getReferenceDate(), forwardCurve, discountCurve, value[0], value[1], value[2], value[3], timeScaling, quotingConvention);
}
}
© 2015 - 2025 Weber Informatics LLC | Privacy Policy