Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library: times
See also: simGBM simHeston

Quantlet: simgOU
Description: Simulation of discrete observations of a generalized Ornstein-Uhlenbeck process via Euler scheme. The process follows the stochastic differential equation: dX(t) = beta (L - X(t)) dt + sigma (X(t)^gamma) dW(t).

Usage: x = simgOU(n,x0,beta,L,rho,gamma,delta)
Input:
n scalar, time. The number of observations is represented by (ceil(n/delta)+1)
x0 scalar, starting value of the process
beta scalar, speed of mean reversion
L scalar, long-term mean
rho scalar, volatility
gamma scalar, scaling factor
delta scalar, time step size. The process is simulated at time points 0, delta, 2*delta, ..., n*delta
Output:
x (n+1) x 1 vector, simulated trajectory

Example:
randomize(123)
library("times")
library("plot")
days = 250
time =(0:days)/days
L = .1
x = 100*simgOU(1,.1,3,L,.29,.5,1/days)
s1 = setmask(time~x,"line","black","thin","solid")
d1 = createdisplay(1,1)
show(d1,1,1,s1)

Result:
A display containing a typical trajectory of a gOU
process is shown.



Author: R. Weron, 20040521 license MD*Tech
(C) MD*TECH Method and Data Technologies, 05.02.2006