  This paper describes a flexible and tractable bottom-up dynamic correlation
modelling framework with a consistent stochastic recovery specification. The
stochastic recovery specification only models the first two moments of the spot
recovery rate as its higher moments have almost no contribution to the loss
distribution and CDO tranche pricing. Observing that only the joint
distribution of default indicators is needed to build the portfolio loss
distribution, we propose a generic class of default indicator copulas to model
CDO tranches, which can be easily calibrated to index tranche prices across
multiple maturities. This correlation modelling framework has the unique
advantage that the joint distribution of default time and other dynamic
properties of the model can be changed separately from the loss distribution
and tranche prices. After calibrating the model to index tranche prices,
existing top-down methods can be applied to the common factor process to
construct very flexible systemic dynamics without changing the already
calibrated tranche prices. This modelling framework therefore combines the best
features of the bottom-up and top-down models: it is fully consistent with all
the single name market information and it admits very rich and flexible spread
dynamics. Numerical results from a non-parametric implementation of this
modelling framework are also presented. The non-parametric implementation
achieved fast and accurate calibration to the index tranches across multiple
maturities even under extreme market conditions. A conditional Markov chain
method is also proposed to construct the systemic dynamics, which supports an
efficient lattice pricing method for dynamic spread instruments. We also showed
how to price tranche options as an example of this fast lattice method.
