The stochastically subordinated Poisson normal process for modelling financial assets

The method of stochastic subordination, or random time indexing, has been recently applied to Wiener process price processes to model financial returns. Previous emphasis in stochastic subordination models has involved explicitly identifying the subordinating process with an observable quantity such as number of trades. In contrast, the approach taken here does not depend on the specific identification of the subordinated time variable, but rather assumes a class of time models and estimates parameters from data. In addition, a simple Markov process is proposed for the characteristic parameter of the subordinating distribution to explain the significant autocorrelation of the squared returns. It is shown, in particular, that the proposed model, while containing only a few more parameters than the commonly used Wiener process models, fits selected financial time series particularly well, characterising the autocorrelation structure and heavy tails, as well as preserving the desirable self-similarity structure, and the existence of risk-neutral measures necessary for objective derivative valuation. Also, it will be shown that the model proposed fits financial time series data better than the popular generalised autoregressive conditional heteroscedasticity models. Additionally, this paper will develop a skew model by replacing the normal variates with Lévy stable variates.