Characteristic function estimation of OrnsteinUhlenbeck-based stochastic volatility models
Continuous-time stochastic volatility models are becoming increasingly popular in finance because of their flexibility in accommodating most stylized facts of financial time series. However, their estimation is difficult because the likelihood function does not have a closed-form expression. A characteristic function-based estimation method for non-Gaussian OrnsteinUhlenbeck-based stochastic volatility models is proposed. Explicit expressions of the characteristic functions for various cases of interest are derived. The asymptotic properties of the estimators are analyzed and their small-sample performance is evaluated by means of a simulation experiment. Finally, two real-data applications show that the superposition of two OrnsteinUhlenbeck processes gives a good approximation to the dependence structure of the process.
characteristic function estimation stochastic volatility ornsteinuhlenbeck process lvy process