setCovarParam (3) Linux Manual Page

QuantLib::LiborForwardModelProcess – libor-forward-model process

Synopsis

LiborForwardModelProcess(Size size, const boost::shared_ptr<IborIndex> &index)

    Disposable<Array> initialValues() const

    returns the initial values of the state variables

    Disposable<Array> drift(Time t, const Array &x) const

    returns the drift part of the equation,
    i.e., $ mu(t, mathrm{x} _t) $

    Disposable<Matrix> diffusion(Time t, const Array &x) const

    returns the diffusion part of the equation,
    i.e.$ igma(t, mathrm{x} _t) $

    Disposable<Matrix> covariance(Time t0, const Array &x0, Time dt) const

    Disposable<Array> apply(const Array &x0, const Array &dx) const

    Disposable<Array> evolve(Time t0, const Array &x0, Time dt, const Array &dw) const

    Size size() const

    returns the number of dimensions of the stochastic process

    Size factors() const

    returns the number of independent factors of the process

    boost::shared_ptr<IborIndex> index() const

    Leg cashFlows(Real amount = 1.0) const

    void setCovarParam(const boost::shared_ptr<LfmCovarianceParameterization> &param)

        boost::shared_ptr<LfmCovarianceParameterization> covarParam() const

    Size nextIndexReset(Time t) const

    const std::vector<Time> &fixingTimes() const

    const std::vector<Date> &fixingDates() const

    const std::vector<Time> &accrualStartTimes() const

    const std::vector<Time> &accrualEndTimes() const

    std::vector<DiscountFactor> discountBond(const std::vector<Rate> &rates) const

Inherits QuantLib::StochasticProcess.

Public Member Functions

LiborForwardModelProcess(Size size, const boost::shared_ptr<IborIndex> &index)

    Disposable<Array> initialValues() const

    returns the initial values of the state variables

    Disposable<Array> drift(Time t, const Array &x) const

    returns the drift part of the equation,
    i.e., $ mu(t, mathrm{x} _t) $

    Disposable<Matrix> diffusion(Time t, const Array &x) const

    returns the diffusion part of the equation,
    i.e.$ igma(t, mathrm{x} _t) $

    Disposable<Matrix> covariance(Time t0, const Array &x0, Time dt) const

    Disposable<Array> apply(const Array &x0, const Array &dx) const

    Disposable<Array> evolve(Time t0, const Array &x0, Time dt, const Array &dw) const

    Size size() const

    returns the number of dimensions of the stochastic process

    Size factors() const

    returns the number of independent factors of the process

    boost::shared_ptr<IborIndex> index() const

    Leg cashFlows(Real amount = 1.0) const

    void setCovarParam(const boost::shared_ptr<LfmCovarianceParameterization> &param)

        boost::shared_ptr<LfmCovarianceParameterization> covarParam() const

    Size nextIndexReset(Time t) const

    const std::vector<Time> &fixingTimes() const

    const std::vector<Date> &fixingDates() const

    const std::vector<Time> &accrualStartTimes() const

    const std::vector<Time> &accrualEndTimes() const

    std::vector<DiscountFactor> discountBond(const std::vector<Rate> &rates) const

Detailed Description

libor-forward-model process

stochastic process of a libor forward model using the rolling forward measure incl. predictor-corrector step

References:

Glasserman, Paul, 2004, Monte Carlo Methods in Financial Engineering, Springer, Section 3.7

Antoon Pelsser, 2000, Efficient Methods for Valuing Interest Rate Derivatives, Springer, 8

Hull, John, White, Alan, 1999, Forward Rate Volatilities, Swap Rate Volatilities and the Implementation of the Libor Market Model (<http://www.rotman.utoronto.ca/~amackay/fin/libormktmodel2.pdf>)

Tests

the correctness is tested by Monte-Carlo reproduction of caplet & ratchet NPVs and comparison with Black pricing.

Warning

this class does not work correctly with Visual C++ 6.

Member Function Documentation

Disposable<Matrix> covariance (Time t0, const Array & x0, Time dt) const [virtual]

returns the covariance $ V(mathrm{x}_{t_0 + Delta t} | mathrm{x}_{t_0} = mathrm{x}_0) $ of the process after a time interval $ Delta t $ according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.

Reimplemented from StochasticProcess.

Disposable<Array> apply (const Array & x0, const Array & dx) const [virtual]

applies a change to the asset value. By default, it returns $ mathrm{x} + Delta mathrm{x} $.

Reimplemented from StochasticProcess.

Disposable<Array> evolve (Time t0, const Array & x0, Time dt, const Array & dw) const [virtual]

returns the asset value after a time interval $ Delta t $ according to the given discretization. By default, it returns [ E(mathrm{x}_0,t_0,Delta t) + S(mathrm{x}_0,t_0,Delta t) dot Delta mathrm{w} ] where $ E $ is the expectation and $ S $ the standard deviation.

Reimplemented from StochasticProcess.

Author

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