net.finmath.montecarlo.assetderivativevaluation.models.BachelierModel Maven / Gradle / Ivy

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/*
 * (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;
import net.finmath.stochastic.Scalar;

/**
 * This class implements a (variant of the) Bachelier 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
 * \[
 * 	d(S/N) = \sigma dW, \quad S(0) = S_{0},
 * \]
 * \[
 * 	dN = r N dt, \quad N(0) = N_{0},
 * \]
 *
 * Note: This implies the dynamic
 * \[
 * 	dS = r S dt + \sigma exp(r t) dW, \quad S(0) = S_{0},
 * \]
 * for \( S \). For The model
 * \[
 * 	dS = r S dt + \sigma dW, \quad S(0) = S_{0},
 * \]
 * see {@link net.finmath.montecarlo.assetderivativevaluation.models.InhomogenousBachelierModel}.
 *
 * The model's implied Bachelier volatility for a given maturity T is
 * volatility * Math.exp(riskFreeRate * optionMaturity)
 *
 * The class provides the model of S to an {@link net.finmath.montecarlo.process.MonteCarloProcess} via the specification of
 * \( f = \text{identity} \), \( \mu = \frac{exp(r \Delta t_{i}) - 1}{\Delta t_{i}} S(t_{i}) \), \( \lambda_{1,1} = \sigma \), i.e.,
 * of the SDE
 * \[
 * 	dX = \mu dt + \lambda_{1,1} dW, \quad X(0) = \log(S_{0}),
 * \]
 * with \( S = X \). See {@link net.finmath.montecarlo.process.MonteCarloProcess} for the notation.
 *
 * @author Christian Fries
 * @version 1.0
 * @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.
 */
public class BachelierModel 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 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 volatility The volatility.
	 */
	public BachelierModel(RandomVariableFactory randomVariableFactory, RandomVariable initialValue, RandomVariable riskFreeRate, RandomVariable volatility) {
		super();
		this.randomVariableFactory = randomVariableFactory;
		this.initialValue = initialValue;
		this.riskFreeRate = riskFreeRate;
		this.volatility = volatility;
	}

	/**
	 * Create a Monte-Carlo simulation using given time discretization.
	 *
	 * @param initialValue Spot value.
	 * @param riskFreeRate The risk free rate.
	 * @param volatility The volatility.
	 */
	public BachelierModel(
			final double initialValue,
			final double riskFreeRate,
			final double volatility) {
		super();

		this.randomVariableFactory = new RandomVariableFromArrayFactory();
		this.initialValue	= randomVariableFactory.createRandomVariable(initialValue);
		this.riskFreeRate	= randomVariableFactory.createRandomVariable(riskFreeRate);
		this.volatility		= randomVariableFactory.createRandomVariable(volatility);
	}

	@Override
	public RandomVariable[] getInitialState(MonteCarloProcess process) {
		return new RandomVariable[] { initialValue };
	}

	@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 newVolatility		= RandomVariableFactory.getRandomVariableOrDefault(newRandomVariableFactory, dataModified.get("volatility"), volatility);

		return new BachelierModel(newRandomVariableFactory, newInitialValue, newRiskFreeRate, newVolatility);
	}

	@Override
	public String toString() {
		return super.toString() + "\n" +
				"BachelierModel:\n" +
				"  initial value...:" + initialValue + "\n" +
				"  risk free rate..:" + riskFreeRate + "\n" +
				"  volatiliy.......:" + volatility;
	}

	/**
	 * Returns the initial value parameter of this model.
	 *
	 * @return Returns the initialValue
	 */
	public RandomVariable getInitialValue() {
		return 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 volatility;
	}

	public RandomVariable getImpliedBachelierVolatility(final double maturity) {
		return volatility.mult(riskFreeRate.mult(maturity).exp());
	}
}