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Stochastic volatility models for financial time series

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Stochastic volatility models are used in mathematical finance to describe the evolution of asset returns, which typically exhibit changing variances over time.

Model description

 

The dataset is  previously analyzed by Harvey et al. (1994), and later by several other authors. The data consist of a time series of daily pound/dollar exchange rates {zt} from the period 01/10/81 to 28/6/85. The series of interest are the daily mean-corrected returns {yt}, given by the transformation

 

yt = log(zt)-log(zt-1) - average[logzi-logzi-1].

 

The stochastic volatility model allows the variance of yt to vary smoothly with time. This is achieved by assuming that yt ~ N(0,st), where st = exp{-0.5(mx+xt)}. Here, the smoothly varying component xt is assumed to be an autoregression.

 

Details

 sdv.pdf

Files

See "Navigation" box to the left.

  • .tpl:  Model file
  • .dat: Data file
  • .pin: Starting values for the numerical optimizer
  • .par: Result file (what you get when you compile and run your model)