VoseTimeGBMVR

See also: Time series in ModelRisk; Fitting in ModelRisk;Univariate Time Series Fit

VoseTimeGBMVR(Reversion Value, Sigma, Alpha, Log Return, Initial Value)

 

 

 

Array function that models a Geometric Brownian Motion (GBM) with Reversion to a fixed value S*.

  • Reversion Value - value towards which the series reverts;

  • Sigma - standard deviation of log returns of underlying Geometric Brownian Motion;

  • Alpha - the mean reversion factor;

  • Log Return - an optional parameter. Function generates log returns if set to TRUE, or variable values if set to FALSE or omitted.

  • Initial Value - starting value (at time zero). The generated time series values will continue on from this value. Should only be provided if the Log Return parameter is set to FALSE or omitted;

As the ModelRisk Time Series functions typically take a lot of parameters, we recommend for these in particular to use the Time Series window.

Equations

where:

 - a sample from a Normal(0,1)

- standard deviation of log returns of underlying Geometric Brownian Motion

- mean reversion factor

S* - value towards which the series reverts

VoseFunctions for this time series

VoseTimeGBMVR - generates an array of random values from this time series.

VoseTimeGBMVRFit - generates an array of random values from this time series fitted to data.

VoseTimeGBMVRFitP - returns the parameters of this time series fitted to data.

 

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