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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.Arrays;
import java.util.Map;
import net.finmath.montecarlo.RandomVariableFactory;
import net.finmath.montecarlo.RandomVariableFromArrayFactory;
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 BlackScholesModel extends AbstractProcessModel {
private final RandomVariableFactory randomVariableFactory;
private final RandomVariable initialValue;
private final RandomVariable riskFreeRate;
private final RandomVariable volatility;
// Cache for arrays provided though AbstractProcessModel
private final RandomVariable[] initialState;
private final RandomVariable[] drift;
private final RandomVariable[] factorLoadings;
/**
* Create a Black-Scholes specification implementing AbstractProcessModel.
*
* @param initialValue Spot value.
* @param riskFreeRate The risk free rate.
* @param volatility The log volatility.
* @param randomVariableFactory The random variable factory used to create random variables from constants.
*/
public BlackScholesModel(
final RandomVariable initialValue,
final RandomVariable riskFreeRate,
final RandomVariable volatility,
final RandomVariableFactory randomVariableFactory) {
super();
this.initialValue = initialValue;
this.volatility = volatility;
this.riskFreeRate = riskFreeRate;
this.randomVariableFactory = randomVariableFactory;
// Cache
initialState = new RandomVariable[] { initialValue.log() };
drift = new RandomVariable[] { riskFreeRate.sub(volatility.squared().div(2)) };
factorLoadings = new RandomVariable[] { volatility };
}
/**
* Create a Monte-Carlo simulation using given time discretization.
*
* @param initialValue Spot value.
* @param riskFreeRate The risk free rate.
* @param volatility The log volatility.
* @param randomVariableFactory The random variable factory used to create random variables from constants.
*/
public BlackScholesModel(
final double initialValue,
final double riskFreeRate,
final double volatility,
final RandomVariableFactory randomVariableFactory) {
this(randomVariableFactory.createRandomVariable(initialValue), randomVariableFactory.createRandomVariable(riskFreeRate), randomVariableFactory.createRandomVariable(volatility), randomVariableFactory);
}
/**
* Create a Black-Scholes model from given parameters.
*
* @param initialValue Spot value.
* @param riskFreeRate The risk free rate.
* @param volatility The log volatility.
*/
public BlackScholesModel(
final double initialValue,
final double riskFreeRate,
final double volatility) {
this(initialValue, riskFreeRate, volatility, new RandomVariableFromArrayFactory());
}
@Override
public RandomVariable[] getInitialState(MonteCarloProcess process) {
return initialState;
}
@Override
public RandomVariable[] getDrift(final MonteCarloProcess process, final int timeIndex, final RandomVariable[] realizationAtTimeIndex, final RandomVariable[] realizationPredictor) {
return drift;
}
@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) {
return riskFreeRate.mult(time).exp();
}
@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 BlackScholesModel getCloneWithModifiedData(final Map dataModified) {
/*
* Determine the new model parameters from the provided parameter map.
*/
final double newInitialValue = dataModified.get("initialValue") != null ? ((Number)dataModified.get("initialValue")).doubleValue() : initialValue.getAverage();
final double newRiskFreeRate = dataModified.get("riskFreeRate") != null ? ((Number)dataModified.get("riskFreeRate")).doubleValue() : getRiskFreeRate().getAverage();
final double newVolatility = dataModified.get("volatility") != null ? ((Number)dataModified.get("volatility")).doubleValue() : getVolatility().getAverage();
return new BlackScholesModel(newInitialValue, newRiskFreeRate, newVolatility, randomVariableFactory);
}
/**
* 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 risk free rate parameter of this model.
*
* @return Returns the riskFreeRate.
*/
public RandomVariable getRiskFreeRate() {
return riskFreeRate;
}
/**
* Returns the volatility parameter of this model.
*
* @return Returns the volatility.
*/
public RandomVariable getVolatility() {
return factorLoadings[0];
}
@Override
public String toString() {
return "BlackScholesModel [initialValue=" + initialValue + ", riskFreeRate=" + riskFreeRate + ", volatility="
+ volatility + ", randomVariableFactory=" + randomVariableFactory + ", initialState="
+ Arrays.toString(initialState) + ", drift=" + Arrays.toString(drift) + ", factorLoadings="
+ Arrays.toString(factorLoadings) + "]";
}
}