Sim.DiffProc (version 2.5)

CEV: Creating Constant Elasticity of Variance (CEV) Models (by Milstein Scheme)

Description

Simulation constant elasticity of variance models by milstein scheme.

Usage

CEV(N, M, t0, T, x0, mu, sigma, gamma, 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.

mu

constant (mu * X(t) :drift coefficient).

sigma

constant positive (sigma * X(t)^gamma :diffusion coefficient).

gamma

constant positive (sigma * X(t)^gamma :diffusion coefficient).

output

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

Value

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

Details

The Constant Elasticity of Variance (CEV) model also derives directly from the linear drift class, the discretization dt = (T-t0)/N. The stochastic differential equation of CEV is : $$dX(t) = mu * X(t)* dt + sigma * X(t)^gamma *dW(t)$$ with mu * X(t) :drift coefficient and sigma * X(t)^gamma :diffusion coefficient, W(t) is Wiener process. This process is quite useful in modeling a skewed implied volatility. In particular,for gamma < 1, the skewness is negative, and for gamma > 1 the skewness is positive. For gamma = 1, the CEV process is a particular version of the geometric Brownian motion.

See Also

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

## Constant Elasticity of Variance Models
## dX(t) = 0.3 *X(t) *dt + 2 * X(t)^1.2 * dW(t)
## One trajectorie
CEV(N=1000,M=1,t0=0,T=1,x0=0.1,mu=0.3,sigma=2,gamma=1.2)