Applied Mathematics Seminar

One of the most perplexing problems that practitioners in empirical Financial Economics have to deal with is that of the non-synchronicity of observed asset prices. Non-synchronicity of asset prices occurs whenever assets trade with finite frequency -- instead of the continuous manner assumed by the underlying theoretical continuous-time diffusion Financial model. The non-synchronicity problem is particularly acute in the high frequency empirical research domain - such as is the rage these days when price arbitrage is the main objective of the large body of practicing arbitragers operating in the world's capital market centers -- such as London, New York, Sydney, and Tokyo. The non-synchronicity problem leads to the bizarre finding of strong positive serial correlation in the returns of asset portfolios -even when the individual assets are serially uncorrelated random walks. This phenomenon necessitates a deeper understanding as to the causes of the observed serial correlation. Indeed, such an understanding can only come about with the use of formal mathematical/statistical representations of the dynamic non-synchronising process itself. In this seminar, two different mathematical models of non-synchronicity are presented, each designed to highlight different aspects of the problem's structure. Also discussed are the more complex representations of inter-temporal non-synchronicity, as well as multivariate non-synchronicity. The seminar is also aimed at demonstrating just how much applied mathematical scope there is in representing the non-synchronicity problem as it arises in Finance.