rcCIR function

Conditional law of the Cox-Ingersoll-Ross process

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.

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

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

Returns

• x: a numeric vector

References

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

Author(s)

Stefano Maria Iacus

See Also

rsCIR

Examples

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