# CEVmodel

CEVmodel computes price and instantaneous variance processes from the CEV model

## Syntax

• S=CEVmodel(t,x)example
• [S,A]=CEVmodel(___)example

## Description

CEVmodel computes price and instantaneous variance for the Constant Elasticity of Variance model [S. Beckers, The Journal of Finance, Vol. 35, No. 3, 1980] via Euler method

 S =CEVmodel(t, x) Example of call of CEVmodel providing only price values.

 [S, A] =CEVmodel(___) Example of call of CEVmodel providing both price and variance values.

## Examples

expand all

### Example of call of CEVmodel providing only price values.

Generates spot prices for the CEV model at times t.

n=1000; dt=1/n;
t=0:dt:1; % discrete time grid
x=100; % initial price value
S=CEVmodel(t,x); % spot prices
plot(t,S)
xlabel('Time')
ylabel('Spot price')
title('CEV model')

### Example of call of CEVmodel providing both price and variance values.

Generates price and instantaneous variance values for the CEV model at times t.

n=1000; dt=1/n;
t=0:dt:1; % discrete time grid
x=100; % initial price value
[S,A]=CEVmodel(t,x); % spot prices and variance
subplot(2,1,1)
plot(t,S)
xlabel('Time')
ylabel('Spot price')
title('CEV model')
subplot(2,1,2)
plot(t,A)
xlabel('Time')
ylabel('Spot variance')
title('CEV model')

## Input Arguments

### t — Discrete time grid. Vector.

Row or column vector.

Data Types: single| double

### x — Initial price value. Scalar.

Data Types: single| double

## Output Arguments

### S —Spot prices.  Vector

Column vector with the same length of t.

### A —Spot variance values.  Vector

Column vector with the same length of t.

The Constant Elasticity of Variance model [S. Beckers, The Journal of Finance, Vol. 35, No. 3, 1980] is given by the following stochastic differential equation $$\left\{\begin{array}{l} dS_t= \sigma \, S_t^{\delta} \, dW_t \\ S_0=x, \end{array}\right.$$ where $\sigma$ and $\delta$ are positive constants and $W$ is a Brownian motion on a filtered probability space. We assume $\sigma=0.3$ and $\delta=1.5$. The instanteneous variance is given by $$A_t=\sigma^2S_t^{2(\delta-1)}.$$