Documentation of 'net.finmath.montecarlo.interestrate.products.SwaptionAnalyticApproximationRebonato' Java class
SwaptionAnalyticApproximationRebonato
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net.finmath.montecarlo.interestrate.products

Class SwaptionAnalyticApproximationRebonato

  • All Implemented Interfaces:
    ProductInterface

    public class SwaptionAnalyticApproximationRebonato
extends AbstractLIBORMonteCarloProduct
    This class implements an analytic swaption valuation formula under a LIBOR market model. The algorithm implemented here is the OIS discounting version of the algorithm described in ISBN 0470047224 (see SwaptionSingleCurveAnalyticApproximation). The approximation assumes that the forward rates (LIBOR) follow a log normal model and that the model provides the integrated instantaneous covariance of the log-forward rates. The getValue method calculates the approximated integrated instantaneous variance of the swap rate, using the approximation of \[ \frac{d log(S(t))}{d log(L(t))} \] according to Rebonato (1999). Since \( L \) is a vector, \( w \) is a gradient (vector). The class then approximates the Black volatility of a swaption via \[ \sigma_S^{2} T := \sum_{i,j} w_{i} \gamma_{i,j} w_{j} \] where \( (\gamma_{i,j})_{i,j = 1,...,m} \) is the covariance matrix of the forward rates. The valuation can be performed in terms of value or implied Black volatility. In this implementation we use the weights as specified by Rebonato (1998) and not the one derived by Hull and White (1999/2000).

    • Constructor Detail

      • SwaptionAnalyticApproximationRebonato

        public SwaptionAnalyticApproximationRebonato(double swaprate,
                                             TimeDiscretizationInterface swapTenor)
        Create an analytic swaption approximation product for log normal forward rate model. Note: It is implicitly assumed that swapTenor.getTime(0) is the exercise date (no forward starting).
        Parameters:
        swaprate - The strike swap rate of the swaption.
        swapTenor - The swap tenor in doubles.

      • SwaptionAnalyticApproximationRebonato

        public SwaptionAnalyticApproximationRebonato(double swaprate,
                                             double[] swapTenor,
                                             SwaptionAnalyticApproximationRebonato.ValueUnit valueUnit)
        Create an analytic swaption approximation product for log normal forward rate model. Note: It is implicitly assumed that swapTenor[0] is the exercise date (no forward starting).
        Parameters:
        swaprate - The strike swap rate of the swaption.
        swapTenor - The swap tenor in doubles.
        valueUnit - The unit of the quantity returned by the getValues method.

    • Method Detail

      • getValue

        public RandomVariableInterface getValue(double evaluationTime,
                                        LIBORModelMonteCarloSimulationInterface model)
        Description copied from class: AbstractLIBORMonteCarloProduct
        This method returns the value random variable of the product within the specified model, evaluated at a given evalutationTime. Note: For a lattice this is often the value conditional to evalutationTime, for a Monte-Carlo simulation this is the (sum of) value discounted to evaluation time. Cashflows prior evaluationTime are not considered.
        Specified by:
        getValue in class AbstractLIBORMonteCarloProduct
        Parameters:
        evaluationTime - The time on which this products value should be observed.
        model - The model used to price the product.
        Returns:
        The random variable representing the value of the product discounted to evaluation time

      • getValues

        public RandomVariableInterface getValues(double evaluationTime,
                                         LIBORMarketModelInterface model)
        Calculates the approximated integrated instantaneous variance of the swap rate, using the approximation d log(S(t))/d log(L(t)) = d log(S(0))/d log(L(0)).
        Parameters:
        evaluationTime - Time at which the product is evaluated.
        model - A model implementing the LIBORModelMonteCarloSimulationInterface
        Returns:
        Depending on the value of value unit, the method returns either the approximated integrated instantaneous variance of the swap rate (ValueUnit.INTEGRATEDVARIANCE) or the value using the Black formula (ValueUnit.VALUE).

      • getLogSwaprateDerivative

        public static java.util.Map<java.lang.String,double[]> getLogSwaprateDerivative(TimeDiscretizationInterface liborPeriodDiscretization,
                                                                                DiscountCurveInterface discountCurveInterface,
                                                                                ForwardCurveInterface forwardCurveInterface,
                                                                                double[] swapTenor)
        This function calculate the partial derivative d log(S) / d log(Lk) for a given swap rate with respect to a vector of forward rates (on a given forward rate tenor). It also returns some useful other quantities like the corresponding discout factors and swap annuities.
        Parameters:
        liborPeriodDiscretization - The libor period discretization.
        discountCurveInterface - The discount curve. If this parameter is null, the discount curve will be calculated from the forward curve.
        forwardCurveInterface - The forward curve.
        swapTenor - The swap tenor.
        Returns:
        A map containing the partial derivatives (key "value"), the discount factors (key "disocuntFactors") and the annuities (key "annuities") as vectors of double[] (indexed by forward rate tenor index starting at swap start)

      • getIntegratedLIBORCovariance

        public static double[][][] getIntegratedLIBORCovariance(LIBORMarketModel model)
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