
PEOU(X, delta, starts = list(r= 1, sigma= 1), leve = 0.95)
r > 0
. We have also shown its exact conditional and stationary densities. In particular, the conditional density p(t,.|x)
is the density of a Gaussian law
with mean = x0 * exp(-r*t)
and variance = ((sigma^2)/(2*r))*(1-exp(-2*r*t))
.
R
has the [dqpr]norm
functions to evaluate the density, the quantiles, and the cumulative distribution or generate pseudo random numbers from the normal distribution.PEABM
Parametric Estimation of Arithmetic Brownian Motion, PEOUexp
Explicit Estimators of Ornstein-Uhlenbeck Model, PEOUG
Parametric Estimation of Hull-White/Vasicek Models, PEBS
Parametric Estimation of model Black-Scholes.## Parametric estimation of Ornstein-Uhlenbeck Model.
## t0 = 0 ,T = 10
data(DATA1)
res <- PEOU(DATA1,delta=0.01,starts=list(r=2,sigma=1),leve = 0.90)
res
OUF(N=1000,M=10,t0=0,T=10,x0=40,r=0.1979284,sigma=3.972637)
points(seq(0,10,length=length(DATA1)),DATA1,type="l",lwd=3,col="red")
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