CEVmodel

CEVmodel computes price and instantaneous variance processes from the CEV model

Syntax

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

example

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

example

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

Examples

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  • 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')
    Click here for the graphical output of this example (link to Ro.S.A. website). Graphical output could not be included in the installation file because toolboxes cannot be greater than 20MB. To load locally the image files, download zip file http://rosa.unipr.it/fsda/images.zip and unzip it to <tt>(docroot)/FSDA/images</tt> or simply run routine <tt>downloadGraphicalOutput.m</tt>

  • 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')
    Click here for the graphical output of this example (link to Ro.S.A. website). Graphical output could not be included in the installation file because toolboxes cannot be greater than 20MB. To load locally the image files, download zip file http://rosa.unipr.it/fsda/images.zip and unzip it to <tt>(docroot)/FSDA/images</tt> or simply run routine <tt>downloadGraphicalOutput.m</tt>

    Input Arguments

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    t — Discrete time grid. Vector.

    Row or column vector.

    Data Types: single| double

    x — Initial price value. Scalar.

    Data Types: single| double

    Output Arguments

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    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.

    More About

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    Additional Details

    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 $$A_t=\sigma^2S_t^{2(\delta-1)}.$$

    References

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