time step of the simulation (discretization). If it is missing a default Dt = (T-t0)/N.
mu
parameter of the HWV and OU; see details.
theta
parameter of the HWV; see details.
sigma
the volatility of the HWV and OU.
...
further arguments for (non-default) methods.
Details
The function HWV returns a trajectory of the Hull-White/Vasicek process starting at x0 at time t0;
i.e., the diffusion process solution of stochastic differential equation:
dX(t) = mu *( theta- X(t)) dt + sigma dW(t)
The function OU returns a trajectory of the Ornstein-Uhlenbeck starting at x0 at time t0;
i.e., the diffusion process solution of stochastic differential equation:
dX(t) = -mu * X(t) dt + sigma dW(t)
Constraints: mu, sigma >0.
Please note that the process is stationary only if mu >0.
Value
X
an visible ts object.
Author(s)
A.C. Guidoum, K. Boukhetala.
References
Vasicek, O. (1977).
An Equilibrium Characterization of the Term Structure.
Journal of Financial Economics, 5, 177–188.
See Also
rcOU and rsOU for conditional and stationary law of Vasicek process are available in sde.
R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
> library(Sim.DiffProc)
Package 'Sim.DiffProc' version 3.2 loaded.
help(Sim.DiffProc) for summary information.
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/Sim.DiffProc/HWV.Rd_%03d_medium.png", width=480, height=480)
> ### Name: HWV
> ### Title: Hull-White/Vasicek, Ornstein-Uhlenbeck process
> ### Aliases: HWV OU HWV.default OU.default
> ### Keywords: sde ts
>
> ### ** Examples
>
> ## Hull-White/Vasicek Models
> ## dX(t) = 4 * (2.5 - X(t)) * dt + 1 *dW(t), X0=10
> set.seed(1234)
>
> X <- HWV(N=1000,M=50,mu = 4, theta = 2.5,sigma = 1,x0=10)
> plot(X,plot.type="single")
> lines(as.vector(time(X)),rowMeans(X),col="red")
>
> ## Ornstein-Uhlenbeck Process
> ## dX(t) = -4 * X(t) * dt + 1 *dW(t) , X0=2
> set.seed(1234)
>
> X <- OU(N=1000,M=50,mu = 4,sigma = 1,x0=10)
> plot(X,plot.type="single")
> lines(as.vector(time(X)),rowMeans(X),col="red")
>
>
>
>
>
> dev.off()
null device
1
>