  In this paper we consider classes of models that have been recently developed
for quantitative finance that involve modelling a highly complex multivariate,
multi-attribute stochastic process known as the Limit Order Book (LOB). The LOB
is the primary data structure recorded each day intra-daily for all assets on
every electronic exchange in the world in which trading takes place. As such,
it represents one of the most important fundamental structures to study from a
stochastic process perspective if one wishes to characterize features of
stochastic dynamics for price, volume, liquidity and other important attributes
for a traded asset. In this paper we aim to adopt the model structure which
develops a stochastic model framework for the LOB of a given asset and to
explain how to perform calibration of this stochastic model to real observed
LOB data for a range of different assets.
