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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 20.01.2004
*/
package net.finmath.montecarlo.assetderivativevaluation.models;
import java.util.Map;
import net.finmath.marketdata.model.curves.DiscountCurve;
import net.finmath.montecarlo.RandomVariableFactory;
import net.finmath.montecarlo.model.AbstractProcessModel;
import net.finmath.montecarlo.process.MonteCarloProcess;
import net.finmath.stochastic.RandomVariable;
/**
* This class implements a Black Scholes Model, that is, it provides the drift and volatility specification
* and performs the calculation of the numeraire (consistent with the dynamics, i.e. the drift).
*
* The model is
* \[
* dS = r S dt + \sigma S dW, \quad S(0) = S_{0},
* \]
* \[
* dN = r N dt, \quad N(0) = N_{0},
* \]
*
* The class provides the model of S to an {@link net.finmath.montecarlo.process.MonteCarloProcess} via the specification of
* \( f = exp \), \( \mu = r - \frac{1}{2} \sigma^2 \), \( \lambda_{1,1} = \sigma \), i.e.,
* of the SDE
* \[
* dX = \mu dt + \lambda_{1,1} dW, \quad X(0) = \log(S_{0}),
* \]
* with \( S = f(X) \). See {@link net.finmath.montecarlo.process.MonteCarloProcess} for the notation.
*
* @author Christian Fries
* @see net.finmath.montecarlo.process.MonteCarloProcess The interface for numerical schemes.
* @see net.finmath.montecarlo.model.ProcessModel The interface for models provinding parameters to numerical schemes.
* @version 1.0
*/
public class BlackScholesModelWithCurves extends AbstractProcessModel {
private final RandomVariable initialValue;
private final RandomVariable volatility;
private final DiscountCurve discountCurveForForwardRate;
private final DiscountCurve discountCurveForDiscountRate;
private final RandomVariableFactory randomVariableFactory;
// Cache for arrays provided though AbstractProcessModel
private final RandomVariable[] initialState;
private final RandomVariable driftAdjustment;
private final RandomVariable[] factorLoadings;
/**
* Create a Black-Scholes specification implementing AbstractProcessModel.
*
* @param initialValue Spot value.
* @param discountCurveForForwardRate The curve used for calcuation of the forward.
* @param volatility The log volatility.
* @param discountCurveForDiscountRate The curve used for calcualtion of the disocunt factor / numeraire.
* @param randomVariableFactory The random variable factory used to create random variables from constants.
*/
public BlackScholesModelWithCurves(
final RandomVariable initialValue,
final DiscountCurve discountCurveForForwardRate,
final RandomVariable volatility,
final DiscountCurve discountCurveForDiscountRate,
final RandomVariableFactory randomVariableFactory) {
this.initialValue = initialValue;
this.volatility = volatility;
this.discountCurveForForwardRate = discountCurveForForwardRate;
this.discountCurveForDiscountRate = discountCurveForDiscountRate;
this.randomVariableFactory = randomVariableFactory;
initialState = new RandomVariable[] { initialValue.log() };
driftAdjustment = volatility.squared().div(-2.0);
factorLoadings = new RandomVariable[] { volatility };
}
/**
* Create a Black-Scholes specification implementing AbstractProcessModel.
*
* @param initialValue Spot value.
* @param discountCurveForForwardRate The curve used for calcuation of the forward.
* @param volatility The log volatility.
* @param discountCurveForDiscountRate The curve used for calcualtion of the disocunt factor / numeraire.
* @param randomVariableFactory The random variable factory used to create random variables from constants.
*/
public BlackScholesModelWithCurves(
final Double initialValue,
final DiscountCurve discountCurveForForwardRate,
final Double volatility,
final DiscountCurve discountCurveForDiscountRate,
final RandomVariableFactory randomVariableFactory) {
this(randomVariableFactory.createRandomVariable(initialValue), discountCurveForForwardRate, randomVariableFactory.createRandomVariable(volatility), discountCurveForDiscountRate, randomVariableFactory);
}
@Override
public RandomVariable[] getInitialState(MonteCarloProcess process) {
return initialState;
}
@Override
public RandomVariable[] getDrift(final MonteCarloProcess process, final int timeIndex, final RandomVariable[] realizationAtTimeIndex, final RandomVariable[] realizationPredictor) {
final double time = process.getTime(timeIndex);
final double timeNext = process.getTime(timeIndex+1);
final double rate = Math.log(discountCurveForForwardRate.getDiscountFactor(time) / discountCurveForForwardRate.getDiscountFactor(timeNext)) / (timeNext-time);
return new RandomVariable[] { driftAdjustment.add(rate) };
}
@Override
public RandomVariable[] getFactorLoading(final MonteCarloProcess process, final int timeIndex, final int component, final RandomVariable[] realizationAtTimeIndex) {
return factorLoadings;
}
@Override
public RandomVariable applyStateSpaceTransform(MonteCarloProcess process, int timeIndex, final int componentIndex, final RandomVariable randomVariable) {
return randomVariable.exp();
}
@Override
public RandomVariable applyStateSpaceTransformInverse(final MonteCarloProcess process, final int timeIndex, final int componentIndex, final RandomVariable randomVariable) {
return randomVariable.log();
}
@Override
public RandomVariable getNumeraire(MonteCarloProcess process, final double time) {
final double discounFactorForDiscounting = discountCurveForDiscountRate.getDiscountFactor(time);
return randomVariableFactory.createRandomVariable(1.0/discounFactorForDiscounting);
}
@Override
public int getNumberOfComponents() {
return 1;
}
@Override
public int getNumberOfFactors() {
return 1;
}
@Override
public RandomVariable getRandomVariableForConstant(final double value) {
return randomVariableFactory.createRandomVariable(value);
}
@Override
public BlackScholesModelWithCurves getCloneWithModifiedData(final Map dataModified) {
/*
* Determine the new model parameters from the provided parameter map.
*/
final RandomVariable newInitialValue = dataModified.get("initialValue") != null ? (RandomVariable)dataModified.get("initialValue") : initialValue;
final RandomVariable newVolatility = dataModified.get("volatility") != null ? (RandomVariable)dataModified.get("volatility") : volatility;
return new BlackScholesModelWithCurves(newInitialValue, discountCurveForForwardRate, newVolatility, discountCurveForDiscountRate, randomVariableFactory);
}
@Override
public String toString() {
return super.toString() + "\n" +
"BlackScholesModel:\n" +
" initial value...:" + initialValue + "\n" +
" forward curve...:" + discountCurveForForwardRate + "\n" +
" discount curve..:" + discountCurveForDiscountRate + "\n" +
" volatiliy.......:" + getVolatility();
}
/**
* Return the initial value of this model.
*
* @return the initial value of this model.
*/
@Override
public RandomVariable[] getInitialValue(final MonteCarloProcess process) {
return new RandomVariable[] { initialValue };
}
/**
* Returns the volatility parameter of this model.
*
* @return Returns the volatility.
*/
public RandomVariable getVolatility() {
return factorLoadings[0];
}
}