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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.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 displaced lognormal 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
* \[
* \mathrm{d}S = r S \mathrm{d}t + \sigma (d \cdot N + S) \mathrm{d}W, \quad S(0) = S_{0},
* \]
* \[
* \mathrm{d}N = r N \mathrm{d}t, \quad N(0) = N_{0},
* \]
*
* Note that
* \[
* \mathrm{d}(S/N) = \sigma (d+S/N) \mathrm{d}W
* \]
* that is
* \[
* \mathrm{d}X = - 1/2 \sigma^2 \mathrm{d}t + \sigma \mathrm{d}W
* \]
* with exp(X) = d + S/N, i.e. S = N ( exp(X)-d ).
*
* The class provides the model of S to an {@link net.finmath.montecarlo.process.MonteCarloProcess}
* via the specification of
* \( S = f(X) = N (exp(X)-d) \), \( \mu = -\frac{1}{2} \sigma^{2} \), \( \lambda_{1,1} = \sigma \), i.e.,
* of the SDE
* \[
* dX = \mu dt + \lambda_{1,1} dW, \quad X(0) = \log(d+S_{0}),
* \]
* with \( N(0) = 1 \). See {@link net.finmath.montecarlo.process.MonteCarloProcess} for the notation.
*
* The model can be interpreted as a linear interpolation of the Black-Scholes model
* {@link net.finmath.montecarlo.assetderivativevaluation.models.BlackScholesModel}
* and the homogeneous Bachelier model
* {@link net.finmath.montecarlo.assetderivativevaluation.models.BachelierModel}.
*
* @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 1.1
*/
public class DisplacedLognomalModel extends AbstractProcessModel {
private final RandomVariableFactory randomVariableFactory;
private final RandomVariable initialValue;
private final RandomVariable riskFreeRate; // Actually the same as the drift (which is not stochastic)
private final RandomVariable displacement;
private final RandomVariable volatility;
/**
* Create a Monte-Carlo simulation using given time discretization.
*
* @param randomVariableFactory The RandomVariableFactory used to generate random variables from constants.
* @param initialValue Spot value.
* @param riskFreeRate The risk free rate.
* @param displacement The displacement parameter d.
* @param volatility The volatility.
*/
public DisplacedLognomalModel(
final RandomVariableFactory randomVariableFactory,
final RandomVariable initialValue,
final RandomVariable riskFreeRate,
final RandomVariable displacement,
final RandomVariable volatility) {
super();
this.randomVariableFactory = randomVariableFactory;
this.initialValue = initialValue;
this.riskFreeRate = riskFreeRate;
this.displacement = displacement;
this.volatility = volatility;
}
/**
* Create a Monte-Carlo simulation using given time discretization.
*
* @param randomVariableFactory The RandomVariableFactory used to generate random variables from constants.
* @param initialValue Spot value.
* @param riskFreeRate The risk free rate.
* @param displacement The displacement parameter d.
* @param volatility The volatility.
*/
public DisplacedLognomalModel(
final RandomVariableFactory randomVariableFactory,
final double initialValue,
final double riskFreeRate,
final double displacement,
final double volatility) {
this(
randomVariableFactory,
randomVariableFactory.createRandomVariable(initialValue),
randomVariableFactory.createRandomVariable(riskFreeRate),
randomVariableFactory.createRandomVariable(displacement),
randomVariableFactory.createRandomVariable(volatility)
);
}
/**
* Create a Monte-Carlo simulation using given time discretization.
*
* @param initialValue Spot value.
* @param riskFreeRate The risk free rate.
* @param displacement The displacement parameter d.
* @param volatility The volatility.
*/
public DisplacedLognomalModel(
final double initialValue,
final double riskFreeRate,
final double displacement,
final double volatility) {
this(new RandomVariableFromArrayFactory(), initialValue, riskFreeRate, displacement, volatility);
}
@Override
public RandomVariable[] getInitialState(MonteCarloProcess process) {
return new RandomVariable[] { initialValue.add(displacement).log() };
}
@Override
public RandomVariable[] getDrift(final MonteCarloProcess process, final int timeIndex, final RandomVariable[] realizationAtTimeIndex, final RandomVariable[] realizationPredictor) {
final RandomVariable[] drift = new RandomVariable[realizationAtTimeIndex.length];
for(int componentIndex = 0; componentIndex dataModified) {
/*
* Determine the new model parameters from the provided parameter map.
*/
final RandomVariableFactory newRandomVariableFactory = (RandomVariableFactory)dataModified.getOrDefault("randomVariableFactory", randomVariableFactory);
final RandomVariable newInitialValue = RandomVariableFactory.getRandomVariableOrDefault(newRandomVariableFactory, dataModified.get("initialValue"), initialValue);
final RandomVariable newRiskFreeRate = RandomVariableFactory.getRandomVariableOrDefault(newRandomVariableFactory, dataModified.get("riskFreeRate"), riskFreeRate);
final RandomVariable newDisplacement = RandomVariableFactory.getRandomVariableOrDefault(newRandomVariableFactory, dataModified.get("displacement"), displacement);
final RandomVariable newVolatility = RandomVariableFactory.getRandomVariableOrDefault(newRandomVariableFactory, dataModified.get("volatility"), volatility);
return new DisplacedLognomalModel(newRandomVariableFactory, newInitialValue, newRiskFreeRate, newDisplacement, newVolatility);
}
@Override
public String toString() {
return "DisplacedLognomalModelExperimental [randomVariableFactory=" + randomVariableFactory + ", initialValue="
+ initialValue + ", riskFreeRate=" + riskFreeRate + ", displacement=" + displacement + ", volatility="
+ volatility + "]";
}
public RandomVariableFactory getRandomVariableFactory() {
return randomVariableFactory;
}
public RandomVariable getInitialValue() {
return initialValue;
}
/**
* Returns the risk free rate parameter of this model.
*
* @return Returns the riskFreeRate.
*/
public RandomVariable getRiskFreeRate() {
return riskFreeRate;
}
public RandomVariable getDisplacement() {
return displacement;
}
/**
* Returns the volatility parameter of this model.
*
* @return Returns the volatility.
*/
public RandomVariable getVolatility() {
return volatility;
}
}