Continuous time stochastic volatility (SV) models provide great fexibility for asset pricing theory and applications to option pricing, however, exact statistical inference poses a great challenge for this type of models. In view of this, our work progresses in two aspects: First and mainly, we shall provide a new framework for continuous time SV modelling, where a unified likelihood based inference procedure is available. This may impress on one that the new framework is only raised for the ease of inference, whereas, as we shall show later, it arises naturally from an interesting empirical study of market microstructure from a chronological perspective. A potential of our new framework is that it may initiate a more realistic direction for the study of market microstructure than does...[ Read more ]

Continuous time stochastic volatility (SV) models provide great fexibility for asset pricing theory and applications to option pricing, however, exact statistical inference poses a great challenge for this type of models. In view of this, our work progresses in two aspects: First and mainly, we shall provide a new framework for continuous time SV modelling, where a unified likelihood based inference procedure is available. This may impress on one that the new framework is only raised for the ease of inference, whereas, as we shall show later, it arises naturally from an interesting empirical study of market microstructure from a chronological perspective. A potential of our new framework is that it may initiate a more realistic direction for the study of market microstructure than does the existing literature in this area. But we have to say that our work is at a preliminary stage, and further investigations are warranted. Second, we study the advantages of gamma processes in continuous time SV modelling under the traditional BNS framework with an emphasis on that both the likelihood based inference procedure and practical financial derivatives pricing can be exactly implemented.