Parameter estimation in continuous stochastic volatility models

Abstract

Continuous-time di usion processes are often used in literature to model dynamics of nancial markets. In such kinds of models a rel- evant role is played by the variance of the process. So assumptions on the functional form of such variance have to be made in order to analyse the distribution of the resulting process and to make inference on the model. In this paper the variance is also modelled by means of a di usion process. This comes out as continuous time approximation of a GARCH(1; 1) process. Inference on the parameters and properties of the involved estimators are discussed under di erent choices of the frequency data. Simulations on the model are also performed.