Andreas Andersson, presents his master thesis

Credit Migration Derivatives

- Modelling of the Underlying Credit Migration Matrices

abstract

In this thesis I develop a model for describing the dynamic behavior
of Credit Migration Matrices under a Point-in-time Rating
Philosophy. Characteristics of the yearly Migration Matrices following
a Point-in-Time Philosophy are presented. Through the introduction of
the concept of Rating Migration Velocity, the characteristics can be
summarized with one quantity. Which is specified by the direction and
the speed of the migrations. The direction of a migration matrix is
the difference between the upgrades and the downgrades.  The speed
capture the magnitude of the migrations, high speed leads to
migrations over several rating classes and low speed leads to
migrations that are close to the diagonal of the migration matrix.
The model I introduce is an Affine Markov Chain Model with Regime
Shifting Migration Matrices that extends the Affine Markov Chain Model
of Hurd and Kuznetsov (2006a). The model can be separated into a
two-dimensional Markov Chain, with two time-homogeneous Markov Chains,
driven by stochastic time changes tau_G(t) ; tau_B(t) . The shift between the
chains are govern by a regime shifting parameter q(t), depending on the
status of the economic cycle. Under this new framework I give
analytical solutions for Credit Derivatives ranging from Defaultable
Bonds to CDSs and CDOs.  Keywords: Dynamic Credit Risk modelling,
Point-in-time Rating Philosophy, Rating Migration Velocity, Affine
Markov Chain Model, Credit Derivatives pricing.