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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 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.ConditionalExpectationEstimator;
import net.finmath.stochastic.RandomVariable;
/**
* A service that allows to estimate conditional expectation via regression.
*
* 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 MonteCarloConditionalExpectationRegression implements ConditionalExpectationEstimator {
/**
* Interface for objects specifying regression basis functions (a vector of random variables).
*
* @author Christian Fries
*/
public interface RegressionBasisFunctions {
RandomVariable[] getBasisFunctions();
}
/**
* Wrapper to an array of RandomVariable[] implementing RegressionBasisFunctions
* @author Christian Fries
*/
public static class RegressionBasisFunctionsGiven implements RegressionBasisFunctions {
private final RandomVariable[] basisFunctions;
public RegressionBasisFunctionsGiven(final RandomVariable[] basisFunctions) {
super();
this.basisFunctions = basisFunctions;
}
@Override
public RandomVariable[] getBasisFunctions() {
return basisFunctions;
}
}
private RegressionBasisFunctions basisFunctionsEstimator = null;
private RegressionBasisFunctions basisFunctionsPredictor = null;
private transient DecompositionSolver solver;
private final transient Object solverLock;
public MonteCarloConditionalExpectationRegression() {
super();
solverLock = new Object(); // Lock for LazyInit of solver.
}
/**
* Creates a class for conditional expectation estimation.
*
* @param basisFunctions A vector of random variables to be used as basis functions.
*/
public MonteCarloConditionalExpectationRegression(final RandomVariable[] basisFunctions) {
this();
basisFunctionsEstimator = new RegressionBasisFunctionsGiven(getNonZeroBasisFunctions(basisFunctions));
basisFunctionsPredictor = basisFunctionsEstimator;
}
/**
* 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 MonteCarloConditionalExpectationRegression(final RandomVariable[] basisFunctionsEstimator, final RandomVariable[] basisFunctionsPredictor) {
this();
this.basisFunctionsEstimator = new RegressionBasisFunctionsGiven(getNonZeroBasisFunctions(basisFunctionsEstimator));
this.basisFunctionsPredictor = new RegressionBasisFunctionsGiven(getNonZeroBasisFunctions(basisFunctionsPredictor));
}
@Override
public RandomVariable getConditionalExpectation(final RandomVariable randomVariable) {
// Get regression parameters x as the solution of XTX x = XT y
final double[] linearRegressionParameters = getLinearRegressionParameters(randomVariable);
// Calculate estimate, i.e. X x
final RandomVariable[] basisFunctions = basisFunctionsPredictor.getBasisFunctions();
RandomVariable conditionalExpectation = basisFunctions[0].mult(linearRegressionParameters[0]);
for(int i=1; i