sde (version 2.0.18)

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

Description

Density, distribution function, quantile function and random generation for the conditional law \(X(t+D_t) | X(t)=x_0\) 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)

Value

x

a numeric vector

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].

Author

Stefano Maria Iacus

Details

This function returns quantities related to the conditional law of the process solution of $${\rm d}X_t = (\theta_1-\theta_2 X_t){\rm d}t + \theta_3\sqrt{X_t}{\rm d}W_t.$$

Constraints: \(2\theta_1> \theta_3^2\), all \(\theta\) positive.

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))