VoseTimeGBMAJVR

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

VoseTimeGBMAJVR(Reversion Value, Sigma, Alpha, MuJ, SigmaJ, PJump, PJumpUp, Log Return, Initial Value)

 

 

 

Array function that models a Geometric Brownian Motion (GBM) time series model with Asymmetric Jumps and 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;

  • 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 - Optional boolean parameter (TRUE/FALSE) specifying whether to return the actual time series (FALSE, default) or log returns (TRUE);

  • 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)

- mean log return of a jump

- standard deviation of log returns of underlying Geometric Brownian Motion

- standard deviation of a jump

- mean reversion factor

S* - value towards which the series reverts

PJump - the probability of a jump in a single period

PJumpUp - the probability that a jump will be upwards

 

VoseFunctions for this time series

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

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

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

 

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