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Transition Generator Add-In
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Scale Matrices to Different
time Periods
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Transition Generator:
Transition Matrix Horizon Interpolator
Convert Transition
Matrices to any other Time Horizon by performing a decomposition of the
non-symmetric Migration Data Matrix into a set of eigenvectors and
eigenvalues.
Transition Matrix=VEtV-1
where
V
are the Eigenvectors of the Transition Matrix
E are the Eigenvalues of the Transition Matrix
Et is the dialogonal Matrix of
Eigenvalues scaled to the ratio of Original Time Period / New Transition
Horizon.
V-1
is the Inverse of the Transition Matrix Eigenvectors.
Note:
Due to the highly unstable nature of non-symmetric matrices, the
Transition Matrix might requires smoothing or "well-conditioning".
In some
rare cases when the horizon is below 0.25
i.e. One Quarter and less , the sum of Migration probabilities for a given
rating rank might not always sum to 100% .
Another approach covered in the Credit-Curve AddIn is to Transform the
Migration into forward defaults (marginal conditional probabilities) by
bootstrapping and then interpolate/extrapolate the vertices according to
desired simulation horizons. (Discrete, Constant). This approach is
perfect if you have implemented a default-mode framework, but will not be
satisfactory in a rating migration framework as this information is
dropped.
A typical Transition Matrix is not symmetric. This requires special
numerical routines.
The Transition Generator is part of the
Risksvr(tm) migration module.
The resulting Migration Ratings are linked to the Credit Spread Curve.
Each Spread Curves is defined as a correlated term structure of vertices with a
starting level, a volatility & corresponding correlations matrix as well as
upper and lower boundary spread levels.
The upper and lower spreads can be defined in three standard ways (absolute
relative and proprietary) spread boundaries and can be defined at the spread
vertex level, the Spread Curve level , per Currency (i.e. Across all
spread curves pertaining to the same currency) or across all spread curves.
Users also have the possibility to select the distribution assumptions for
the simulation of spread data.
Spreads can thus be defined as absolute or relative stochastic processes with a
Lognormal, normal, t-distribution, triangular, exponential, poisson or pareto
distribution
Download Transition Generator Zip File
Zip file includes:
TransitionGenerator.xll
(Add-In), spreadsheet, on-line help and Calculation Principles.
Download Individual Components:
