Sim.DiffProc (version 2.5)

ROU: Creating Radial Ornstein-Uhlenbeck Process (by Milstein Scheme)

Description

Simulation the radial ornstein-uhlenbeck process by milstein scheme.

Usage

ROU(N, M, t0, T, x0, theta, output = FALSE)

Arguments

N

size of process.

M

number of trajectories.

t0

initial time.

T

final time.

x0

initial value of the process at time t0.

theta

constant positive.

output

if output = TRUE write a output to an Excel (.csv).

Value

• data.frame(time,x) and plot of process.

Details

The radial Ornstein-Uhlenbeck process is the solution to the stochastic differential equation :$$dX(t) = (theta * X(t)^-(1) - X(t)) * dt + dW(t)$$ With (theta * X(t)^-1 - X(t)) :drift coefficient and 1 :diffusion coefficient, the discretization dt = (T-t0)/N, W(t) is Wiener process.

See Also

CEV Constant Elasticity of Variance Models, CIR Cox-Ingersoll-Ross Models, CIRhy modified CIR and hyperbolic Process, CKLS Chan-Karolyi-Longstaff-Sanders Models, DWP Double-Well Potential Model, GBM Model of Black-Scholes, HWV Hull-White/Vasicek Models, INFSR Inverse of Feller s Square Root models, JDP Jacobi Diffusion Process, PDP Pearson Diffusions Process, diffBridge Diffusion Bridge Models, snssde Simulation Numerical Solution of SDE.

Examples

## Radial Ornstein-Uhlenbeck 
## dX(t) = (0.05*X(t)^(-1) - X(t)) *dt + dW(t)
## One trajectorie
 ROU(N=1000,M=1,T=1,t0=0,x0=1,theta=0.05)