VoseTimeGBMAJ

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

VoseTimeGBMAJ(Mu, Sigma, MuJ, SigmaJ, PJump, PJumpUp, Initial Value)

 

 

 

Array function that models a Geometric Brownian Motion (GBM) with Asymmetric Jumps.

  • Mu - mean log return of underlying Geometric Brownian Motion;

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

  • MuJ - mean log return of a jump;

  • SigmaJ - standard deviation of a jump;

  • PJump - the probability of a jump in a single period;

  • PJumpUp - the probability that a jump will be upwards;

  • 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)

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

- mean log return of underlying Geometric Brownian Motion

- mean log return of a jump

-  standard deviation of log return of underlying Geometric Brownian Motion;

- standard deviation of a jump;

PJump -the probability of a jump in a single period;

PJumpUp - the probability that a jump will be upwards.

VoseFunctions for this time series

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

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

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

 

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