Interface FiniteDifferenceInterestRateModel

All Superinterfaces:
FiniteDifferenceModel, Model
All Known Implementing Classes:
FDMHullWhiteModel
public interface FiniteDifferenceInterestRateModel extends FiniteDifferenceModel
Base interface for finite-difference interest-rate models.

The interface is designed to remain close to the philosophy of the Monte Carlo interest-rate framework of finmath while exposing the additional ingredients required by a partial-differential-equation discretization.

A model implementing this interface is assumed to satisfy the following two principles:

  • it fits the initially observed term structure automatically through an underlying bootstrapped AnalyticModel,
  • it admits a finite-dimensional Markovian state representation, so that the PDE is solved on a grid of state variables rather than on a full curve of maturities.

More precisely, the model is described by a state vector

X_t = (X_t^{(1)}, \ldots, X_t^{(d)})

evolving under dynamics of the form

dX_t = \mu(t,X_t)\,dt + \lambda(t,X_t)\,dW_t,

where the drift vector \mu and factor-loading matrix \lambda are returned by getDrift(double, double...) and getFactorLoading(double, double...). Observable term-structure quantities are reconstructed from the state. In particular, forward rates are obtained through

F(t;T_1,T_2) = \Phi(t,T_1,T_2,X_t),

where the forwarding curve is identified explicitly in the multi-curve setting.

The interface does not encode a short-rate-only point of view. In particular, no method like getShortRate(...) is required at this level. This keeps the contract suitable for short-rate models, Gaussian HJM / Cheyette models, and other Markovian term-structure specifications.

The default boundary implementation returns StandardBoundaryCondition.none() in every spatial direction. Model-specific classes may override this when Dirichlet or Neumann boundary information is available analytically.

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Author:
Alessandro Gnoatto

  • Method Details

    • getAnalyticModel

      AnalyticModel getAnalyticModel()
      Returns the analytic multi-curve model used as the initial condition of the stochastic term-structure model.

      The returned AnalyticModel is assumed to contain the bootstrapped market curves used to anchor the model to the observed initial term structure.

      Returns:
      The initial analytic multi-curve model.

    • getInitialValue

      double[] getInitialValue()
      Returns the initial value of the Markovian state variables.
      Returns:
      The initial state vector.

    • getDrift

      double[] getDrift(double time, double... stateVariables)
      Returns the drift vector of the Markovian state process.

      This method provides the deterministic part of the state dynamics

      dX_t = \mu(t,X_t)\,dt + \lambda(t,X_t)\,dW_t.

      Parameters:
      time - The current time.
      stateVariables - The current state vector.
      Returns:
      The drift vector at the given state.

    • getFactorLoading

      double[][] getFactorLoading(double time, double... stateVariables)
      Returns the factor-loading matrix of the Markovian state process.

      If d denotes the state dimension and m the Brownian dimension, then the returned array has shape d x m.

      Parameters:
      time - The current time.
      stateVariables - The current state vector.
      Returns:
      The factor-loading matrix at the given state.

    • getDiscountBond

      double getDiscountBond(double time, double maturity, double... stateVariables)
      Returns the value at time time of the discount bond maturing at maturity, conditional on the current model state.

      In a multi-curve setting this method refers to the discounting curve.

      Parameters:
      time - The evaluation time.
      maturity - The maturity of the discount bond.
      stateVariables - The current state vector.
      Returns:
      The discount bond value.

    • getForwardRate

      double getForwardRate(String forwardCurveName, double time, double periodStart, double periodEnd, double... stateVariables)
      Returns the simply compounded forward rate associated with a given forwarding curve and accrual period.

      This is the finite-difference analogue of the Monte Carlo getLibor(...) philosophy. The forwarding curve is identified explicitly because, in a multi-curve framework, it is in general distinct from the discount curve.

      Parameters:
      forwardCurveName - The name of the forwarding curve.
      time - The evaluation time.
      periodStart - The start of the accrual period.
      periodEnd - The end of the accrual period.
      stateVariables - The current state vector.
      Returns:
      The forward rate for the specified accrual period.

    • getLibor

      default double getLibor(String forwardCurveName, double time, double periodStart, double periodEnd, double... stateVariables)
      Alias for getForwardRate(String, double, double, double, double...) using the Monte Carlo terminology.
      Parameters:
      forwardCurveName - The name of the forwarding curve.
      time - The evaluation time.
      periodStart - The start of the accrual period.
      periodEnd - The end of the accrual period.
      stateVariables - The current state vector.
      Returns:
      The forward rate for the specified accrual period.

    • getCloneWithModifiedSpaceTimeDiscretization

      FiniteDifferenceInterestRateModel getCloneWithModifiedSpaceTimeDiscretization(SpaceTimeDiscretization spaceTimeDiscretization)
      Returns a clone of the model using a modified space-time discretization.
      Parameters:
      spaceTimeDiscretization - The new space-time discretization.
      Returns:
      A clone with the modified discretization.

    • getBoundaryConditionsAtLowerBoundary

      default BoundaryCondition[] getBoundaryConditionsAtLowerBoundary(FiniteDifferenceInterestRateProduct product, double time, double... stateVariables)
      Returns the lower-boundary conditions for the current product and state.

      The default implementation returns StandardBoundaryCondition.none() in every spatial direction.

      Parameters:
      product - The product being priced.
      time - The current time.
      stateVariables - The current boundary state.
      Returns:
      Boundary conditions at the lower boundary.

    • getBoundaryConditionsAtUpperBoundary

      default BoundaryCondition[] getBoundaryConditionsAtUpperBoundary(FiniteDifferenceInterestRateProduct product, double time, double... stateVariables)
      Returns the upper-boundary conditions for the current product and state.

      The default implementation returns StandardBoundaryCondition.none() in every spatial direction.

      Parameters:
      product - The product being priced.
      time - The current time.
      stateVariables - The current boundary state.
      Returns:
      Boundary conditions at the upper boundary.