finMath lib documentation
net.finmath.montecarlo.interestrate.modelplugins

## Class LIBORCovarianceModelStochasticVolatility

• public class LIBORCovarianceModelStochasticVolatility
extends AbstractLIBORCovarianceModelParametric
Simple stochastic volatility model, using a process $d\lambda(t) = \nu \lambda(t) \left( \rho \mathrm{d} W_{1}(t) + \sqrt{1-\rho^{2}} \mathrm{d} W_{2}(t) \right) \text{,}$ where $$\lambda(0) = 1$$ to scale all factor loadings $$f_{i}$$ returned by a given covariance model. The model constructed is $$\lambda(t) F(t)$$ where $$\lambda(t)$$ is the (Euler discretization of the) above process and $$F = ( f_{1}, \ldots, f_{m} )$$ is the factor loading from the given covariance model. The process uses the first two factors of the Brownian motion provided by an object implementing BrownianMotionInterface. This can be used to generate correlations to other objects. If you like to reuse a factor of another Brownian motion use a BrownianMotionView to delegate $$( \mathrm{d} W_{1}(t) , \mathrm{d} W_{2}(t) )$$ to a different object. The parameter of this model is a joint parameter vector, consisting of the parameter vector of the given base covariance model and appending the parameters ν and ρ at the end. If this model is not calibrateable, its parameter vector is that of the covariance model, i.e., ν and ρ will be not part of the calibration. For an illustration of its usage see the associated unit test.
Author:
Christian Fries
• ### Constructor Detail

• #### LIBORCovarianceModelStochasticVolatility

public LIBORCovarianceModelStochasticVolatility(AbstractLIBORCovarianceModelParametric covarianceModel,
BrownianMotionInterface brownianMotion,
double nu,
double rho,
boolean isCalibrateable)
Create a modification of a given AbstractLIBORCovarianceModelParametric with a stochastic volatility scaling.
Parameters:
covarianceModel - A given AbstractLIBORCovarianceModelParametric.
brownianMotion - An object implementing BrownianMotionInterface with at least two factors. This class uses the first two factors, but you may use BrownianMotionView to change this.
nu - The initial value for ν, the volatility of the volatility.
rho - The initial value for ρ the correlation to the first factor.
isCalibrateable - If true, the parameters ν and ρ are parameters. Note that the covariance model (covarianceModel) may have its own parameter calibration settings.
• ### Method Detail

int component,
RandomVariableInterface[] realizationAtTimeIndex)
Description copied from class: AbstractLIBORCovarianceModel
Return the factor loading for a given time index and component index. The factor loading is the vector fi such that the scalar product
fjfk = fj,1fk,1 + ... + fj,mfk,m
is the instantaneous covariance of the component j and k.
Specified by:
Parameters:
component - The index of the component i.
realizationAtTimeIndex - The realization of the stochastic process (may be used to implement local volatility/covariance/correlation models).
Returns:

int component,
int factor,
RandomVariableInterface[] realizationAtTimeIndex)
Description copied from class: AbstractLIBORCovarianceModel
Returns the pseudo inverse of the factor matrix.
Specified by: