[Yuima-commits] r798 - pkg/yuima/man

[noreply at r-forge.r-project.org]

Author: hirokimasuda
Date: 2022-06-22 07:30:00 +0200 (Wed, 22 Jun 2022)
New Revision: 798

Added:
   pkg/yuima/man/simCIR.Rd
Log:
added

Added: pkg/yuima/man/simCIR.Rd
===================================================================
--- pkg/yuima/man/simCIR.Rd	                        (rev 0)
+++ pkg/yuima/man/simCIR.Rd	2022-06-22 05:30:00 UTC (rev 798)
@@ -0,0 +1,73 @@
+% Generated by roxygen2
+\name{simCIR}
+\alias{simCIR}
+
+\title{Simulation of the Cox-Ingersoll-Ross diffusion}
+
+\description{
+This is a function to simulate a Cox-Ingersoll-Ross process given via the SDE 
+
+	\eqn{\mathrm{d} X_t = (\alpha-\beta X_t)\mathrm{d} t + \sqrt{\gamma X_t}\mathrm{d} W_t}
+		
+	with a Brownian motion \eqn{(W_t)_{t\geq 0}} and parameters \eqn{\alpha,\beta,\gamma>0.} We use an exact CIR simulator for \eqn{(X_{t_j} )_{j=1,\dots,n}} through the non-central chi-squares distribution.
+}
+
+\usage{
+simCIR(time.points, n, h, alpha, beta, gamma, equi.dist=FALSE )
+}
+
+\arguments{
+  \item{alpha, beta, gamma}{
+  numbers given as in the SDE above. 
+  }
+  \item{equi.dist}{a logical value indicating whether the sampling points are equidistant (default \code{equi.dist=FALSE}).
+  }
+  
+  \item{n}{
+  a number indicating the quantity of sampling points in the case \code{equi.dist=TRUE}.
+  }
+  \item{h}{
+  a number indicating the step size in the case \code{equi.dist=TRUE}.  
+  }
+  \item{time.points}{
+  a numeric vector of sampling times (necessary if \code{equi.dist=FALSE}).
+  }
+}
+
+\value{
+  A numeric matrix containing the realization of \eqn{(t_0,X_{t_0}),\dots, (t_n,X_{t_n})} with \eqn{t_j} denoting the \eqn{j}-th sampling times.
+
+}
+
+\references{
+S. J. A. Malham and A. Wiese. Chi-square simulation of the CIR process
+and the Heston model. Int. J. Theor. Appl. Finance, 16(3):1350014, 38,
+2013.
+}
+
+\author{
+Nicole Hufnagel 
+
+Contacts: \email{nicole.hufnagel at math.tu-dortmund.de}
+}
+
+\examples{
+##You always need the parameters alpha, beta and gamma
+##Additionally e.g. time.points
+data <- simCIR(alpha=3,beta=1,gamma=1,time.points = c(0,0.1,0.2,0.25,0.3))
+## or n, number of observations, h, distance between observations, and equi.dist=TRUE
+data <- simCIR(alpha=3,beta=1,gamma=1,n=1000,h=0.1,equi.dist=TRUE)
+plot(data[1,],data[2,], type="l",col=4)
+## If you input every value and equi.dist=TRUE, time.points are not used for the simulations.
+data <- simCIR(alpha=3,beta=1,gamma=1,n=1000,h=0.1, time.points = c(0,0.1,0.2,0.25,0.3), equi.dist=TRUE)
+## If you leave equi.dist=FALSE, the parameters n and h are not used for the simulation.
+data <- simCIR(alpha=3,beta=1,gamma=1,n=1000,h=0.1, time.points = c(0,0.1,0.2,0.25,0.3))
+}
+
+\keyword{CIR diffusion}
+
+
+
+
+
+