VoseTimeGBM

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

VoseTimeGBM(Mu, Sigma, Initial Value, {Time Stamps}, Log Return)

 

 

 

Array function that models a Geometric Brownian Motion (GBM) time series model. GBM is usually the default starting point for a time series of a non-negative financial variable - like a stock price, exchange rate or interest rate. It assumes that the fractional changes in the variable between periods are independent, random variables following a Normal distribution.

  • Mu - mean log return;

  • Sigma- standard deviation of log returns;

  • 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;

  • {Time Stamps} - an array of time stamps (optional);

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

- if   is the value of the variable at time t, then is the log return defined as

- log return mean

- log return standard deviation

VoseFunctions for this time series

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

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

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

 

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