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finmath lib is a Mathematical Finance Library in Java.
It provides algorithms and methodologies related to mathematical finance.
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/*
* (c) Copyright Christian P. Fries, Germany. Contact: [email protected].
*
* Created on 13.08.2004
*/
package net.finmath.montecarlo.conditionalexpectation;
import org.apache.commons.math3.linear.Array2DRowRealMatrix;
import org.apache.commons.math3.linear.ArrayRealVector;
import org.apache.commons.math3.linear.DecompositionSolver;
import org.apache.commons.math3.linear.SingularValueDecomposition;
import net.finmath.stochastic.RandomVariable;
import net.finmath.stochastic.Scalar;
/**
* A service that allows to estimate conditional expectation via regression.
*
* This implementation uses a localization weight derived from the dependent variable.
* The regression only considers sample paths where \( - M < y_{i} < M \) where M is a multiple of the standard deviation of y.
*
* In oder to estimate the conditional expectation, basis functions have to be specified.
*
* The class can either estimate and predict the conditional expectation within
* the same simulation (which will eventually introduce a small foresight bias)
* or use a different simulation for estimation (using basisFunctionsEstimator)
* to predict conditional expectation within another simulation
* (using basisFunctionsPredictor). In the latter case, the
* basis functions have to correspond to the same entities, however, generated in
* different simulations (number of path, etc., may be different).
*
* @author Christian Fries
* @version 1.0
*/
public class MonteCarloConditionalExpectationRegressionLocalizedOnDependents extends MonteCarloConditionalExpectationRegression {
private final double standardDeviations;
/**
* Creates a class for conditional expectation estimation.
*
* @param basisFunctionsEstimator A vector of random variables to be used as basis functions for estimation.
* @param basisFunctionsPredictor A vector of random variables to be used as basis functions for prediction.
* @param standardDeviations A standard deviation parameter for the weight function.
*/
public MonteCarloConditionalExpectationRegressionLocalizedOnDependents(final RandomVariable[] basisFunctionsEstimator, final RandomVariable[] basisFunctionsPredictor, final double standardDeviations) {
super(basisFunctionsEstimator, basisFunctionsPredictor);
this.standardDeviations = standardDeviations;
}
/**
* Creates a class for conditional expectation estimation.
*
* @param basisFunctionsEstimator A vector of random variables to be used as basis functions for estimation.
* @param standardDeviations A standard deviation parameter for the weight function.
*/
public MonteCarloConditionalExpectationRegressionLocalizedOnDependents(final RandomVariable[] basisFunctionsEstimator, final double standardDeviations) {
super(basisFunctionsEstimator);
this.standardDeviations = standardDeviations;
}
public MonteCarloConditionalExpectationRegressionLocalizedOnDependents() {
this(null, 4.0);
}
/**
* Creates a class for conditional expectation estimation.
*
* @param basisFunctions A vector of random variables to be used as basis functions.
*/
public MonteCarloConditionalExpectationRegressionLocalizedOnDependents(final RandomVariable[] basisFunctions) {
this(basisFunctions, 4.0);
}
/**
* Creates a class for conditional expectation estimation.
*
* @param basisFunctionsEstimator A vector of random variables to be used as basis functions for estimation.
* @param basisFunctionsPredictor A vector of random variables to be used as basis functions for prediction.
*/
public MonteCarloConditionalExpectationRegressionLocalizedOnDependents(final RandomVariable[] basisFunctionsEstimator, final RandomVariable[] basisFunctionsPredictor) {
this(basisFunctionsEstimator, basisFunctionsPredictor, 4.0);
}
/**
* Return the solution x of XTX x = XT y for a given y.
* @TODO Performance upon repeated call can be optimized by caching XTX.
*
* @param dependents The sample vector of the random variable y.
* @return The solution x of XTX x = XT y.
*/
@Override
public double[] getLinearRegressionParameters(RandomVariable dependents) {
final RandomVariable localizerWeights = dependents.squared().sub(Math.pow(dependents.getStandardDeviation()*standardDeviations,2.0)).choose(new Scalar(0.0), new Scalar(1.0));
// Localize basis functions
final RandomVariable[] basisFunctionsNonLocalized = getBasisFunctionsEstimator().getBasisFunctions();
final RandomVariable[] basisFunctions = new RandomVariable[basisFunctionsNonLocalized.length];
for(int i=0; i