dCIR: The Cox-Ingersoll-Ross process

In Uffe-H-Thygesen/SDEtools: Utilities for Stochastic Differential Equations

The Cox-Ingersoll-Ross process

Description

Density, distribution function, quantile function, and random generation for the transition probabilities in the Cox-Ingersoll-Ross process given by the stochastic differential equation dX = lambda*(xi-X)*dt + gamma*sqrt(X)*dB (interpreted in the sense of Ito (default) or Stratonovich (optional))

Usage

dCIR(x,x0,lambda,xi,gamma,t,Stratonovich=FALSE,log=FALSE)

pCIR(x,x0,lambda,xi,gamma,t,Stratonovich=FALSE,log.p=FALSE,lower.tail=TRUE)

qCIR(p,x0,lambda,xi,gamma,t,Stratonovich=FALSE,log.p=FALSE,lower.tail=TRUE)

rCIR(n,x0,lambda,xi,gamma,t,Stratonovich=FALSE)

Arguments

x, q	Target state, assumed >= 0
x0	Initial state, assumed > 0
lambda	Rate parameter, assumed > 0
xi	Mean parameter, assumed > 0
gamma	Noise intensity parameters, assumed > 0
t	Terminal time, assumed > 0
Stratonovich	Logical, TRUE for Stratonovich, FALSE (default) for Ito
log, log.p	Logical, if TRUE, probabilities/densities are given as log(p). Default is FALSE
lower.tail	Logical; if TRUE (default) probabilities are P(X<=x); otherise, P(X>x).
p	Probability, assumed >= 0 and <= 1.

Value

dCIR gives the transition probability density, pCIR gives the distribution of the transitio probability, qCIR gives the quantiles, and rCIR samples a random terminal point.

The length of the result is determined by n for rCIR, and is the maximum of the lengths of the numerical arguments for the other functions.

Examples

x <- sort(rCIR(100,1,1,1,1,1))
par(mfrow=c(1,2))
plot(x,dCIR(x,1,1,1,1,1),ylab="p.d.f.")
F <- pCIR(x,1,1,1,1,1)
plot(x,F)
lines(qCIR(F,1,1,1,1,1),F)

Uffe-H-Thygesen/SDEtools documentation built on Jan. 15, 2025, 6:41 p.m.