| 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 | |
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)
A display containing a typical trajectory of a gOU process is shown.