Uniform Ergodicity and Exponential α-Mixing for Continuous Time Stochastic Volatility Model

Uniform Ergodicity and Exponential α-Mixing for Continuous Time Stochastic Volatility Model

A continuous time stochastic volatility model for financial assets suggested by Barndorff-Nielsen and Shephard (2001) is considered, where the volatility process is modelled as an Ornstein-Uhlenbeck type process driven by a general L´evy process and the price process is then obtained by using an independent Brownian motion as the driving noise. The uniform ergodicity of the volatility process and exponential α-mixing properties of the log price processes of given continuous time stochastic volatility models are obtained.

A continuous time stochastic volatility model for financial assets suggested by Barndorff-Nielsen and Shephard (2001) is considered, where the volatility process is modelled as an Ornstein-Uhlenbeck type process driven by a general L´evy process and the price process is then obtained by using an independent Brownian motion as the driving noise. The uniform ergodicity of the volatility process and exponential α-mixing properties of the log price processes of given continuous time stochastic volatility models are obtained.