/*
* (c) Copyright Christian P. Fries, Germany. All rights reserved. Contact: email@christian-fries.de.
*
* Created on 20.01.2004
*/
package net.finmath.montecarlo.assetderivativevaluation;
import java.util.ArrayList;
import java.util.Map;
import net.finmath.exception.CalculationException;
import net.finmath.montecarlo.BrownianMotion;
import net.finmath.montecarlo.BrownianMotionInterface;
import net.finmath.montecarlo.model.AbstractModel;
import net.finmath.montecarlo.process.AbstractProcess;
import net.finmath.montecarlo.process.ProcessEulerScheme;
import net.finmath.stochastic.RandomVariableInterface;
import net.finmath.time.TimeDiscretization;
import net.finmath.time.TimeDiscretizationInterface;
/**
* This class glues together a <code>BlackScholeModel</code> and a Monte-Carlo implementation of a <code>AbstractProcess</code>
* and forms a Monte-Carlo implementation of the Black-Scholes Model by implementing <code>AssetModelMonteCarloSimulationInterface</code>.
*
* 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 <code>{@link net.finmath.montecarlo.process.AbstractProcessInterface}</code> 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.AbstractProcessInterface} for the notation.
*
* @author Christian Fries
* @see net.finmath.montecarlo.process.AbstractProcessInterface The interface for numerical schemes.
* @see net.finmath.montecarlo.model.AbstractModelInterface The interface for models provinding parameters to numerical schemes.
*/
public class MonteCarloBlackScholesModel implements AssetModelMonteCarloSimulationInterface {
private final BlackScholesModel model;
private final double initialValue;
private final int seed = 3141;
/**
* 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(
TimeDiscretizationInterface timeDiscretization,
int numberOfPaths,
double initialValue,
double riskFreeRate,
double volatility) {
super();
this.initialValue = initialValue;
// Create the model
model = new BlackScholesModel(initialValue, riskFreeRate, volatility);
// Create a corresponding MC process
AbstractProcess process = new ProcessEulerScheme(new BrownianMotion(timeDiscretization, 1 /* numberOfFactors */, numberOfPaths, seed));
// Link model and process for delegation
process.setModel(model);
model.setProcess(process);
}
/**
* 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 process The process discretization scheme which should be used for the simulation.
*/
public MonteCarloBlackScholesModel(
double initialValue,
double riskFreeRate,
double volatility,
AbstractProcess process) {
super();
this.initialValue = initialValue;
// Create the model
model = new BlackScholesModel(initialValue, riskFreeRate, volatility);
// Link model and process for delegation
process.setModel(model);
model.setProcess(process);
}
/* (non-Javadoc)
* @see net.finmath.montecarlo.assetderivativevaluation.AssetModelMonteCarloSimulationInterface#getAssetValue(double, int)
*/
@Override
public RandomVariableInterface getAssetValue(double time, int assetIndex) throws CalculationException {
return getAssetValue(getTimeIndex(time), assetIndex);
}
/* (non-Javadoc)
* @see net.finmath.montecarlo.assetderivativevaluation.AssetModelMonteCarloSimulationInterface#getAssetValue(int, int)
*/
@Override
public RandomVariableInterface getAssetValue(int timeIndex, int assetIndex) throws CalculationException {
return model.getProcess().getProcessValue(timeIndex, assetIndex);
}
/* (non-Javadoc)
* @see net.finmath.montecarlo.assetderivativevaluation.AssetModelMonteCarloSimulationInterface#getNumeraire(int)
*/
@Override
public RandomVariableInterface getNumeraire(int timeIndex) throws CalculationException {
double time = getTime(timeIndex);
return model.getNumeraire(time);
}
/* (non-Javadoc)
* @see net.finmath.montecarlo.assetderivativevaluation.AssetModelMonteCarloSimulationInterface#getNumeraire(double)
*/
@Override
public RandomVariableInterface getNumeraire(double time) throws CalculationException {
return model.getNumeraire(time);
}
/* (non-Javadoc)
* @see net.finmath.montecarlo.MonteCarloSimulationInterface#getMonteCarloWeights(double)
*/
@Override
public RandomVariableInterface getMonteCarloWeights(double time) throws CalculationException {
return getMonteCarloWeights(getTimeIndex(time));
}
/* (non-Javadoc)
* @see net.finmath.montecarlo.assetderivativevaluation.AssetModelMonteCarloSimulationInterface#getNumberOfAssets()
*/
@Override
public int getNumberOfAssets() {
return 1;
}
/* (non-Javadoc)
* @see net.finmath.montecarlo.assetderivativevaluation.AssetModelMonteCarloSimulationInterface#getCloneWithModifiedData(java.util.Map)
*/
@Override
public AssetModelMonteCarloSimulationInterface getCloneWithModifiedData(Map<String, Object> dataModified) {
/*
* Determine the new model parameters from the provided parameter map.
*/
double newInitialTime = dataModified.get("initialTime") != null ? ((Number)dataModified.get("initialTime")).doubleValue() : getTime(0);
double newInitialValue = dataModified.get("initialValue") != null ? ((Number)dataModified.get("initialValue")).doubleValue() : initialValue;
double newRiskFreeRate = dataModified.get("riskFreeRate") != null ? ((Number)dataModified.get("riskFreeRate")).doubleValue() : model.getRiskFreeRate();
double newVolatility = dataModified.get("volatility") != null ? ((Number)dataModified.get("volatility")).doubleValue() : model.getVolatility();
int newSeed = dataModified.get("seed") != null ? ((Number)dataModified.get("seed")).intValue() : seed;
/*
* Create a new model with the new model parameters
*/
BrownianMotionInterface brownianMotion;
if(dataModified.get("seed") != null) {
// The seed has changed. Hence we have to create a new BrownianMotion.
brownianMotion = new BrownianMotion(this.getTimeDiscretization(), 1, this.getNumberOfPaths(), newSeed);
}
else
{
// The seed has not changed. We may reuse the random numbers (Brownian motion) of the original model
brownianMotion = model.getProcess().getBrownianMotion();
}
double timeShift = newInitialTime - getTime(0);
if(timeShift != 0) {
ArrayList<Double> newTimes = new ArrayList<Double>();
newTimes.add(newInitialTime);
for(Double time : model.getProcess().getBrownianMotion().getTimeDiscretization()) if(time > newInitialTime) newTimes.add(time);
TimeDiscretizationInterface newTimeDiscretization = new TimeDiscretization(newTimes);
brownianMotion = brownianMotion.getCloneWithModifiedTimeDiscretization(newTimeDiscretization);
}
AbstractProcess process = new ProcessEulerScheme(brownianMotion);
return new MonteCarloBlackScholesModel(newInitialValue, newRiskFreeRate, newVolatility, process);
}
/* (non-Javadoc)
* @see net.finmath.montecarlo.assetderivativevaluation.AssetModelMonteCarloSimulationInterface#getCloneWithModifiedSeed(int)
*/
@Override
public AssetModelMonteCarloSimulationInterface getCloneWithModifiedSeed(int seed) {
// Create a corresponding MC process
AbstractProcess process = new ProcessEulerScheme(new BrownianMotion(this.getTimeDiscretization(), 1 /* numberOfFactors */, this.getNumberOfPaths(), seed));
return new MonteCarloBlackScholesModel(initialValue, model.getRiskFreeRate(), model.getVolatility(), process);
}
/* (non-Javadoc)
* @see net.finmath.montecarlo.MonteCarloSimulationInterface#getNumberOfPaths()
*/
@Override
public int getNumberOfPaths() {
return model.getProcess().getNumberOfPaths();
}
/* (non-Javadoc)
* @see net.finmath.montecarlo.MonteCarloSimulationInterface#getTimeDiscretization()
*/
@Override
public TimeDiscretizationInterface getTimeDiscretization() {
return model.getProcess().getTimeDiscretization();
}
/* (non-Javadoc)
* @see net.finmath.montecarlo.MonteCarloSimulationInterface#getTime(int)
*/
@Override
public double getTime(int timeIndex) {
return model.getProcess().getTime(timeIndex);
}
/* (non-Javadoc)
* @see net.finmath.montecarlo.MonteCarloSimulationInterface#getTimeIndex(double)
*/
@Override
public int getTimeIndex(double time) {
return model.getProcess().getTimeIndex(time);
}
/* (non-Javadoc)
* @see net.finmath.montecarlo.MonteCarloSimulationInterface#getRandomVariableForConstant(double)
*/
@Override
public RandomVariableInterface getRandomVariableForConstant(double value) {
return model.getProcess().getBrownianMotion().getRandomVariableForConstant(value);
}
/* (non-Javadoc)
* @see net.finmath.montecarlo.MonteCarloSimulationInterface#getMonteCarloWeights(int)
*/
@Override
public RandomVariableInterface getMonteCarloWeights(int timeIndex) throws CalculationException {
return model.getProcess().getMonteCarloWeights(timeIndex);
}
/**
* Returns the {@link AbstractModel} used for this Monte-Carlo simulation.
*
* @return the model
*/
public BlackScholesModel getModel() {
return model;
}
}