rcCIR {sde} | R Documentation |
Density, distribution function, quantile function and random generation for the conditional law Xt+Dt|Xt=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)
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]. |
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, theta's>0
.
x |
a numeric vector |
This package is a companion to the book Simulation and Inference for Stochastic Differential Equation, Springer, NY.
Stefano Maria Iacus
Cox, J.C., Ingersoll, J.E., Ross, S.A. (1985) A theory of the term structure of interest rates, Econometrica, 53, 385-408.
rcCIR(n=1, Dt=0.1, x0=1, theta=c(6,2,2))