rcCIR: Conditional law of the Cox-Ingersoll-Ross process

In sde: Simulation and Inference for Stochastic Differential Equations

Conditional law of the Cox-Ingersoll-Ross process

Description

Density, distribution function, quantile function and random generation for the conditional law X(t+D_t) | X(t)=x0 of the Cox-Ingersoll-Ross process.

Usage

dcCIR(x, Dt, x0, theta, log = FALSE)
pcCIR(x, Dt, x0, theta, lower.tail = TRUE, log.p = FALSE) 
qcCIR(p, Dt, x0, theta, lower.tail = TRUE, log.p = FALSE)
rcCIR(n=1, Dt, x0, theta)

Arguments

x	vector of quantiles.
p	vector of probabilities.
Dt	lag or time.
x0	the value of the process at time t; see details.
theta	parameter of the Ornstein-Uhlenbeck process; see details.
n	number of random numbers to generate from the conditional distribution.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are P[X <= x]; otherwise P[X > x].

Details

This function returns quantities related to the conditional law of the process solution of

dX_t = (theta[1]-theta[2]*Xt)*dt + theta[3]*sqrt(X_t)*dWt.

Constraints: 2*theta[1]> theta[3]^2, all theta positive.

Value

x	a numeric vector

Author(s)

Stefano Maria Iacus

References

Cox, J.C., Ingersoll, J.E., Ross, S.A. (1985) A theory of the term structure of interest rates, Econometrica, 53, 385-408.

See Also

rsCIR

Examples

rcCIR(n=1, Dt=0.1, x0=1, theta=c(6,2,2))

sde documentation built on Sept. 9, 2022, 3:07 p.m.