A normal inverse Gaussian model for a risky asset with dependence

We present a new construction of the normal inverse Gaussian (NIG) fractal activity time model for a risky asset. The construction uses superpositions of diffusion processes and allows for specified exact NIG marginal distributions of the returns and flexible and tractable dependence structure including short or long range dependence. In the case of finite superposition, the fractal activity time is asymptotically self-similar, which is a desired feature seen in practice. The support for the distributional and dependence features of the risky asset model is provided by the data of currency exchange rates.