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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.marketdata.model.volatility.caplet;
import java.time.LocalDate;
import net.finmath.functions.AnalyticFormulas;
import net.finmath.marketdata.model.AnalyticModel;
import net.finmath.marketdata.model.curves.DiscountCurve;
import net.finmath.marketdata.model.curves.ForwardCurve;
import net.finmath.marketdata.model.volatilities.VolatilitySurface;
import net.finmath.marketdata.model.volatility.caplet.smile.LinearSmileInterpolater;
import net.finmath.time.daycount.DayCountConvention;
/**
* This class implements a caplet volatility surface.
*
* @author Daniel Willhalm
* @author Christian Fries (review and fixes)
*/
public class CapletVolatilitySurface implements VolatilitySurface {
private final String name;
private final LocalDate referenceDate;
private final QuotingConvention volatilityConvention;
private final double[][] volatilityMatrix;
private final double[] maturityVector;
private final double[] strikeVector;
private final ForwardCurve forwardCurve;
private final DiscountCurve discountCurve;
private final DayCountConvention daycountConvention;
/**
* The constructor of the caplet volatility surface class.
* A volatility matrix is used to create the surface
*
* @param name The name of the surface.
* @param referenceDate The reference date of the surface.
* @param volatilityMatrix The matrix with caplet volatilities as entries.
* @param maturityVector The maturities of the rows of the volatility matrix.
* @param strikeVector The caplet strikes.
* @param forwardCurve The forward curve.
* @param volatilityConvention The volatility convention.
* @param discountCurve The discount curve.
*/
public CapletVolatilitySurface(final String name, final LocalDate referenceDate, final double[][] volatilityMatrix, final double[] maturityVector, final double[] strikeVector, final ForwardCurve forwardCurve, final QuotingConvention volatilityConvention, final DiscountCurve discountCurve) {
this.name = name;
this.referenceDate = referenceDate;
this.forwardCurve = forwardCurve;
this.discountCurve = discountCurve;
this.volatilityMatrix = volatilityMatrix;
this.maturityVector = maturityVector;
this.strikeVector = strikeVector;
this.volatilityConvention = volatilityConvention;
daycountConvention = null;
}
/**
* The constructor of the caplet volatility surface class.
* A single volatility is used and all matrix entries will be that value.
* This constructor is used if we want to price a cap given a cap volatility.
*
* @param name The name of the surface.
* @param referenceDate The reference date of the surface.
* @param volatility The volatility.
* @param maturityVector The maturities of the rows of the volatility matrix.
* @param strikeVector The caplet strikes.
* @param forwardCurve The forward curve.
* @param volatilityConvention The volatility convention.
* @param discountCurve The discount curve.
*/
public CapletVolatilitySurface(final String name, final LocalDate referenceDate, final double volatility, final double[] maturityVector, final double[] strikeVector, final ForwardCurve forwardCurve, final QuotingConvention volatilityConvention, final DiscountCurve discountCurve) {
this.name = name;
this.referenceDate = referenceDate;
this.forwardCurve = forwardCurve;
this.discountCurve = discountCurve;
volatilityMatrix = new double[maturityVector.length][strikeVector.length];
for (int i = 0; i < maturityVector.length; i++) {
for (int j = 0; j < strikeVector.length; j++) {
volatilityMatrix[i][j] = volatility;
}
}
this.maturityVector = maturityVector;
this.strikeVector = strikeVector;
this.volatilityConvention = volatilityConvention;
daycountConvention = null;
}
/**
* Method that returns the volatility value.
*
* @param maturity The desired maturity.
* @param strike The desired strike
* @param quotingConvention The desired quoting convention.
* @return the volatility value for the given maturity, strike and quoting convention.
*/
@Override
public double getValue(final double maturity, final double strike, final QuotingConvention quotingConvention) {
double distance = Math.abs(maturityVector[0] - maturity);
int closestIndex = 0;
for(int i = 1; i < maturityVector.length; i++){
if(Math.abs(maturityVector[i] - maturity) < distance){
closestIndex = i;
distance = Math.abs(maturityVector[i] - maturity);
}
}
// TODO The inter and extra polater should be made flexible at some point. Right now only one exists
final LinearSmileInterpolater linearSmileInterpolater = new LinearSmileInterpolater(volatilityMatrix, strikeVector);
return linearSmileInterpolater.calculateInterpolatedExtrapolatedSmileVolatility(strike, closestIndex);
}
@Override
public double getValue(final AnalyticModel model, final double maturity, final double strike, final QuotingConvention quotingConvention) {
if(maturity == 0) {
return 0;
}
double value;
double distance = Math.abs(maturityVector[0] - maturity);
int closestIndex = 0;
for(int i = 1; i < maturityVector.length; i++){
if(Math.abs(maturityVector[i] - maturity) < distance){
closestIndex = i;
distance = Math.abs(maturityVector[i] - maturity);
}
}
if(distance == 0) {
final LinearSmileInterpolater linearSmileInterpolater = new LinearSmileInterpolater(volatilityMatrix, strikeVector);
value = linearSmileInterpolater.calculateInterpolatedExtrapolatedSmileVolatility(strike, closestIndex);
}
else {
int maturityGreaterEqualIndex = closestIndex;
if(maturityGreaterEqualIndex < 0) {
maturityGreaterEqualIndex = -maturityGreaterEqualIndex-1;
}
if(maturityGreaterEqualIndex > maturityVector.length-1) {
maturityGreaterEqualIndex = maturityVector.length-1;
}
final double adjustedStrike = this.getForwardCurve().getValue(model, maturityVector[maturityGreaterEqualIndex]) + (strike - this.getForwardCurve().getValue(model, maturity));
final LinearSmileInterpolater linearSmileInterpolater = new LinearSmileInterpolater(volatilityMatrix, strikeVector);
value = linearSmileInterpolater.calculateInterpolatedExtrapolatedSmileVolatility(adjustedStrike, maturityGreaterEqualIndex);
}
return convertFromTo(model, maturity, strike, value, this.getQuotingConvention(), quotingConvention);
}
@Override
public String getName() {
return name;
}
@Override
public QuotingConvention getQuotingConvention() {
return volatilityConvention;
}
@Override
public LocalDate getReferenceDate() {
return referenceDate;
}
public ForwardCurve getForwardCurve() {
return forwardCurve;
}
public DiscountCurve getDiscountCurve() {
return discountCurve;
}
//from abstract class AbstractVolatilitySurface from finmath library
/**
* Convert the value of a caplet from one quoting convention to another quoting convention.
*
* @param model An analytic model providing the context when fetching required market date.
* @param optionMaturity Option maturity of the caplet.
* @param optionStrike Option strike of the caplet.
* @param value Value of the caplet given in the form of fromQuotingConvention.
* @param fromQuotingConvention The quoting convention of the given value.
* @param toQuotingConvention The quoting convention requested.
* @return Value of the caplet given in the form of toQuotingConvention.
*/
public double convertFromTo(final AnalyticModel model, final double optionMaturity, final double optionStrike, final double value, final QuotingConvention fromQuotingConvention, final QuotingConvention toQuotingConvention) {
if(fromQuotingConvention.equals(toQuotingConvention)) {
return value;
}
if(discountCurve == null) {
throw new IllegalArgumentException("Missing discount curve. Conversion of QuotingConvention requires forward curve and discount curve to be set.");
}
if(forwardCurve == null) {
throw new IllegalArgumentException("Missing forward curve. Conversion of QuotingConvention requires forward curve and discount curve to be set.");
}
final double periodStart = optionMaturity;
final double periodEnd = periodStart + forwardCurve.getPaymentOffset(periodStart);
final double forward = forwardCurve.getForward(model, periodStart);
double daycountFraction;
if(daycountConvention != null) {
final LocalDate startDate = referenceDate.plusDays((int)Math.round(periodStart*365));
final LocalDate endDate = referenceDate.plusDays((int)Math.round(periodEnd*365));
daycountFraction = daycountConvention.getDaycountFraction(startDate, endDate);
}
else {
daycountFraction = forwardCurve.getPaymentOffset(periodStart);
}
final double payoffUnit = discountCurve.getDiscountFactor(optionMaturity+forwardCurve.getPaymentOffset(optionMaturity)) * daycountFraction;
if(toQuotingConvention.equals(QuotingConvention.PRICE) && fromQuotingConvention.equals(QuotingConvention.VOLATILITYLOGNORMAL)) {
return AnalyticFormulas.blackScholesGeneralizedOptionValue(forward, value, optionMaturity, optionStrike, payoffUnit);
}
else if(toQuotingConvention.equals(QuotingConvention.PRICE) && fromQuotingConvention.equals(QuotingConvention.VOLATILITYNORMAL)) {
return AnalyticFormulas.bachelierOptionValue(forward, value, optionMaturity, optionStrike, payoffUnit);
}
else if(toQuotingConvention.equals(QuotingConvention.VOLATILITYLOGNORMAL) && fromQuotingConvention.equals(QuotingConvention.PRICE)) {
return AnalyticFormulas.blackScholesOptionImpliedVolatility(forward, optionMaturity, optionStrike, payoffUnit, value);
}
else if(toQuotingConvention.equals(QuotingConvention.VOLATILITYNORMAL) && fromQuotingConvention.equals(QuotingConvention.PRICE)) {
return AnalyticFormulas.bachelierOptionImpliedVolatility(forward, optionMaturity, optionStrike, payoffUnit, value);
}
else {
return convertFromTo(model, optionMaturity, optionStrike, convertFromTo(model, optionMaturity, optionStrike, value, fromQuotingConvention, QuotingConvention.PRICE), QuotingConvention.PRICE, toQuotingConvention);
}
}
/**
* Convert the value of a caplet from one quoting convention to another quoting convention.
*
* @param optionMaturity Option maturity of the caplet.
* @param optionStrike Option strike of the caplet.
* @param value Value of the caplet given in the form of fromQuotingConvention.
* @param fromQuotingConvention The quoting convention of the given value.
* @param toQuotingConvention The quoting convention requested.
* @return Value of the caplet given in the form of toQuotingConvention.
*/
public double convertFromTo(final double optionMaturity, final double optionStrike, final double value, final QuotingConvention fromQuotingConvention, final QuotingConvention toQuotingConvention) {
return convertFromTo(null, optionMaturity, optionStrike, value, fromQuotingConvention, toQuotingConvention);
}
}