On the use of non-linear transformations in Stochastic Volatility models

Stochastic Volatility models have been considered as a real alternative to conditional variance models, assuming that volatility follows a process different from the observed one. However, issues like the unobservable nature of volatility and the creation of “rich” dynamics give rise to the use of non-linear transformations for the volatility process. The Box–Cox transformation and its Yeo–Johnson variation, by nesting both the linear and the non-linear case, can be considered as natural functions to specify non-linear Stochastic Volatility models. In this framework, a fully Bayesian approach is used for parametric and log–volatility estimation. The new models are then investigated for their within-sample and out-of-sample performance against alternative Stochastic Volatility models using real financial data series.