Stochastic volatility models for financial time series



ADMB Files
Code: sdv.tpl
Data: sdv.dat
Initial values: sdv.pin
All required files (DOS): sdv.zip
All required files (linux): sdv.tar.gz
Results: sdv.par


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Model description

Stochastic volatility models are used in mathematical finance to describe the evolution of asset returns, which typically exhibit changing variances over time. As an illustration we use a dataset 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 follow an autoregression
xt = bxt-1 + et,

where et ~ N(0,s2). Further details about the model can be found here: sdv.pdf.