Stochastic volatility models for financial time series

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

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Under linux
Command line option: -ilmn 5.

Results: Computation times
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BUGS : 1.7 hours ; (Meyer & Yu, 2000, Table 1).

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Otter Research

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.