Sim.DiffProc (version 2.5)

Besselp: Creating Bessel process (by Milstein Scheme)

Description

Simulation Besselp process by milstein scheme.

Usage

Besselp(N, M, t0, T, x0, alpha, 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.

alpha

constant positive alpha >=2.

output

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

Value

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

Details

The stochastic differential equation of Bessel process is : $$dX(t) = (alpha-1)/(2*X(t)) * dt + dW(t)$$ with (alpha-1)/(2*X(t)) :drift coefficient and 1 :diffusion coefficient, W(t) is Wiener process, and the discretization dt = (T-t0)/N. Constraints: alpha >= 2 and x0 =! 0.

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, ROU Radial Ornstein-Uhlenbeck Process, diffBridge Diffusion Bridge Models, snssde Simulation Numerical Solution of SDE.

Examples

## Bessel Process
## alpha = 4
## dX(t) = 3/(2*x) * dt + dW(t)
## One trajectorie
Besselp(N=1000,M=1,t0=0,T=100,x0=1,alpha=4,output=FALSE)