# Stochastic volatility models for financial time series

Filed under:
Finance

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 {

*z*} from the period 01/10/81 to 28/6/85. The series of interest are the daily mean-corrected returns {

_{t}*y*}, given by the transformation

_{t}

*y*= log(

_{t}*z*)-log(

_{t}*z*) - average[log

_{t-1}*z*-log

_{i}*z*].

_{i-1}The stochastic volatility model allows the variance of

*y*to vary smoothly with time. This is achieved by assuming that

_{t}*y*~ N(0,

_{t}*s*), where

_{t}*s*= exp{-0.5(

_{t}*m*+

_{x}*x*)}. Here, the smoothly varying component

_{t}*x*is assumed to be an autoregression.

_{t}

### Details

### 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)