rcOU function

Ornstein-Uhlenbeck or Vasicek process conditional law

Density, distribution function, quantile function, and random generation for the conditional law $X(t+Dt) | X(t)=x0$ of the Ornstein-Uhlenbeck process, also known as the Vasicek process.

dcOU(x, Dt, x0, theta, log = FALSE)
pcOU(x, Dt, x0, theta, lower.tail = TRUE, log.p = FALSE) 
qcOU(p, Dt, x0, theta, lower.tail = TRUE, log.p = FALSE)
rcOU(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: $theta[2]>0, theta[3]>0$.

Please note that the process is stationary only if $theta[2]>0$.

Returns

• x: a numeric vector

References

Uhlenbeck, G. E., Ornstein, L. S. (1930) On the theory of Brownian motion, Phys. Rev., 36, 823-841.

Vasicek, O. (1977) An Equilibrium Characterization of the Term Structure, Journal of Financial Economics, 5, 177-188.

Author(s)

Stefano Maria Iacus

See Also

rsOU

Examples

rcOU(n=1, Dt=0.1, x0=1, theta=c(0,2,1))