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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;
import java.util.Map;
import net.finmath.exception.CalculationException;
import net.finmath.montecarlo.BrownianMotion;
import net.finmath.montecarlo.BrownianMotionFromMersenneRandomNumbers;
import net.finmath.montecarlo.assetderivativevaluation.models.BlackScholesModel;
import net.finmath.montecarlo.process.EulerSchemeFromProcessModel;
import net.finmath.montecarlo.process.MonteCarloProcess;
import net.finmath.montecarlo.process.MonteCarloProcessFromProcessModel;
import net.finmath.stochastic.RandomVariable;
import net.finmath.time.TimeDiscretization;
/**
* This class glues together a BlackScholeModel and a Monte-Carlo implementation of a MonteCarloProcessFromProcessModel
* and forms a Monte-Carlo implementation of the Black-Scholes Model by implementing AssetModelMonteCarloSimulationModel.
*
* 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 MonteCarloBlackScholesModel extends MonteCarloAssetModel {
/*
* The default seed
*/
private static final int seed = 3141;
/**
* Create a Monte-Carlo simulation using given process discretization scheme.
*
* @param initialValue Spot value
* @param riskFreeRate The risk free rate
* @param volatility The log volatility
* @param brownianMotion The brownian motion driving the model.
*/
public MonteCarloBlackScholesModel(
final double initialValue,
final double riskFreeRate,
final double volatility,
final BrownianMotion brownianMotion) {
super(new BlackScholesModel(initialValue, riskFreeRate, volatility), brownianMotion);
}
/**
* Create a Monte-Carlo simulation using given time discretization.
*
* @param timeDiscretization The time discretization.
* @param numberOfPaths The number of Monte-Carlo path to be used.
* @param initialValue Spot value.
* @param riskFreeRate The risk free rate.
* @param volatility The log volatility.
*/
public MonteCarloBlackScholesModel(
final TimeDiscretization timeDiscretization,
final int numberOfPaths,
final double initialValue,
final double riskFreeRate,
final double volatility) {
this(
initialValue, riskFreeRate, volatility,
new BrownianMotionFromMersenneRandomNumbers(
timeDiscretization, 1 /* numberOfFactors */, numberOfPaths, seed));
}
/**
* Create a Monte-Carlo simulation using given time discretization.
*
* @param model The model.
* @param process The process.
*/
private MonteCarloBlackScholesModel(
final BlackScholesModel model,
final MonteCarloProcess process) {
super(model, process);
}
@Override
public RandomVariable getAssetValue(final double time, final int assetIndex) throws CalculationException {
final int timeIndex = getTimeIndex(time);
if(timeIndex < 0) {
throw new IllegalArgumentException("The model does not provide an interpolation of simulation time (time given was " + time + ").");
}
return getAssetValue(timeIndex, assetIndex);
}
@Override
public MonteCarloBlackScholesModel getCloneWithModifiedData(final Map dataModified) {
final MonteCarloProcess process = getProcess();
/*
* Create a new model with the new model parameters.
*/
final BlackScholesModel newModel = getModel().getCloneWithModifiedData(dataModified);
/*
* Create a new BrownianMotion, if requested.
*/
final int newSeed = dataModified.get("seed") != null ? ((Number)dataModified.get("seed")).intValue() : seed;
BrownianMotion newBrownianMotion;
if(dataModified.get("seed") != null) {
// The seed has changed. Hence we have to create a new BrownianMotionLazyInit.
newBrownianMotion = new BrownianMotionFromMersenneRandomNumbers(this.getTimeDiscretization(), 1, this.getNumberOfPaths(), newSeed);
}
else {
// The seed has not changed. We may reuse the random numbers (Brownian motion) of the original model
newBrownianMotion = (BrownianMotion)process.getStochasticDriver();
}
final double newInitialTime = dataModified.get("initialTime") != null ? ((Number)dataModified.get("initialTime")).doubleValue() : getTime(0);
final double timeShift = newInitialTime - getTime(0);
if(timeShift != 0) {
final TimeDiscretization newTimeDiscretization = process.getStochasticDriver().getTimeDiscretization().getTimeShiftedTimeDiscretization(timeShift);
newBrownianMotion = newBrownianMotion.getCloneWithModifiedTimeDiscretization(newTimeDiscretization);
}
// Create a corresponding MC process
final MonteCarloProcessFromProcessModel newProcess = new EulerSchemeFromProcessModel(newModel, new BrownianMotionFromMersenneRandomNumbers(this.getTimeDiscretization(), 1 /* numberOfFactors */, this.getNumberOfPaths(), seed));
return new MonteCarloBlackScholesModel(newModel, newProcess);
}
@Override
public AssetModelMonteCarloSimulationModel getCloneWithModifiedSeed(final int seed) {
// Create a corresponding MC process
final MonteCarloProcessFromProcessModel process = new EulerSchemeFromProcessModel(getModel(), new BrownianMotionFromMersenneRandomNumbers(this.getTimeDiscretization(), 1 /* numberOfFactors */, this.getNumberOfPaths(), seed));
return new MonteCarloBlackScholesModel(getModel(), process);
}
/**
* Returns the {@link BlackScholesModel} used for this Monte-Carlo simulation.
*
* @return the model
*/
public BlackScholesModel getModel() {
return (BlackScholesModel)super.getModel();
}
}