com.opengamma.analytics.financial.model.option.pricing.fourier.GaussianCharacteristicExponent.java Source code

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Here is the source code for com.opengamma.analytics.financial.model.option.pricing.fourier.GaussianCharacteristicExponent.java

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/**
 * Copyright (C) 2009 - present by OpenGamma Inc. and the OpenGamma group of companies
 * 
 * Please see distribution for license.
 */
package com.opengamma.analytics.financial.model.option.pricing.fourier;

import static com.opengamma.analytics.math.ComplexMathUtils.add;
import static com.opengamma.analytics.math.ComplexMathUtils.multiply;
import static com.opengamma.analytics.math.ComplexMathUtils.square;

import org.apache.commons.lang.Validate;

import com.opengamma.analytics.math.function.Function1D;
import com.opengamma.analytics.math.number.ComplexNumber;

/**
 * This class represents the characteristic exponent for a Brownian motion driven by normally-distributed increments
 * $$
 * \begin{align*}
 * \phi_X &= E\left[e^{iuX}\right]\\
 * &= \frac{1}{\sqrt{2\pi}\sigma}\int_{-\infty}^{\infty} e^{iux} \exp\left(-\frac{(x - \mu)^2}{2\sigma^2}\right)\\
 * %&= \exp\left({iu\mu - \tfrac{1}{2}\sigma^2 u^2}\right)
 * \end{align*}
 * $$
 * and
 * $$
 * \begin{align*}
 * \phi_{X_t}(u) &= [\phi_X(u)]^t \\
 * &= \exp\left(t\left(iu\mu - \frac{\sigma^2 u^2}{2}\right)\right)
 * \end{align*}
 * $$
 * 
 */
public class GaussianCharacteristicExponent implements CharacteristicExponent {
    private final double _mu;
    private final double _sigma;

    /**
     * 
     * @param mu The mean of the Gaussian distribution
     * @param sigma The standard deviation of the Gaussian distribution, not negative or zero
     */
    public GaussianCharacteristicExponent(final double mu, final double sigma) {
        Validate.isTrue(sigma > 0.0, "sigma > 0");
        _mu = mu;
        _sigma = sigma;
    }

    @Override
    public Function1D<ComplexNumber, ComplexNumber> getFunction(final double t) {
        return new Function1D<ComplexNumber, ComplexNumber>() {
            @Override
            public ComplexNumber evaluate(ComplexNumber x) {
                return getValue(x, t);
            }
        };
    }

    @Override
    public ComplexNumber getValue(ComplexNumber u, double t) {
        Validate.isTrue(t > 0.0, "t > 0");
        Validate.notNull(u, "u");
        final ComplexNumber temp = multiply(_sigma, u);
        final ComplexNumber res = add(multiply(u, new ComplexNumber(0, _mu)), multiply(-0.5, multiply(temp, temp)));
        return multiply(t, res);
    }

    @Override
    public Function1D<ComplexNumber, ComplexNumber[]> getAdjointFunction(final double t) {
        return new Function1D<ComplexNumber, ComplexNumber[]>() {
            @Override
            public ComplexNumber[] evaluate(ComplexNumber x) {
                return getCharacteristicExponentAdjoint(x, t);
            }
        };
    }

    @Override
    public ComplexNumber[] getCharacteristicExponentAdjoint(final ComplexNumber u, final double t) {
        final ComplexNumber[] res = new ComplexNumber[3];
        res[0] = getValue(u, t);
        res[1] = multiply(u, new ComplexNumber(0.0, t));
        res[2] = multiply(-_sigma * t, square(u));
        return res;
    }

    /**
     * 
     * @return $\infty$
     */
    @Override
    public double getLargestAlpha() {
        return Double.POSITIVE_INFINITY;
    }

    /**
     * 
     * @return $-\infty$
     */
    @Override
    public double getSmallestAlpha() {
        return Double.NEGATIVE_INFINITY;
    }

    /**
     * Gets the mean.
     * @return the mean
     */
    public double getMu() {
        return _mu;
    }

    /**
     * Gets the standard deviation.
     * @return the standard deviation
     */
    public double getSigma() {
        return _sigma;
    }

    @Override
    public int hashCode() {
        final int prime = 31;
        int result = 1;
        long temp;
        temp = Double.doubleToLongBits(_mu);
        result = prime * result + (int) (temp ^ (temp >>> 32));
        temp = Double.doubleToLongBits(_sigma);
        result = prime * result + (int) (temp ^ (temp >>> 32));
        return result;
    }

    @Override
    public boolean equals(final Object obj) {
        if (this == obj) {
            return true;
        }
        if (obj == null) {
            return false;
        }
        if (getClass() != obj.getClass()) {
            return false;
        }
        final GaussianCharacteristicExponent other = (GaussianCharacteristicExponent) obj;
        if (Double.doubleToLongBits(_mu) != Double.doubleToLongBits(other._mu)) {
            return false;
        }
        return Double.doubleToLongBits(_sigma) == Double.doubleToLongBits(other._sigma);
    }

}