Abstract: One of the most important tasks in the risk
management is the correct determination of probability of default
(PD) of particular financial subjects. In this paper a possibility of
determination of financial institution’s PD according to the creditscoring
models is discussed. The paper is divided into the two parts.
The first part is devoted to the estimation of the three different
models (based on the linear discriminant analysis, logit regression
and probit regression) from the sample of almost three hundred US
commercial banks. Afterwards these models are compared and
verified on the control sample with the view to choose the best one.
The second part of the paper is aimed at the application of the chosen
model on the portfolio of three key Czech banks to estimate their
present financial stability. However, it is not less important to be able
to estimate the evolution of PD in the future. For this reason, the
second task in this paper is to estimate the probability distribution of
the future PD for the Czech banks. So, there are sampled randomly
the values of particular indicators and estimated the PDs’ distribution,
while it’s assumed that the indicators are distributed according to the
multidimensional subordinated Lévy model (Variance Gamma model
and Normal Inverse Gaussian model, particularly). Although the
obtained results show that all banks are relatively healthy, there is
still high chance that “a financial crisis” will occur, at least in terms
of probability. This is indicated by estimation of the various quantiles
in the estimated distributions. Finally, it should be noted that the
applicability of the estimated model (with respect to the used data) is
limited to the recessionary phase of the financial market.
Abstract: Collateralized Debt Obligations are not as widely used
nowadays as they were before 2007 Subprime crisis. Nonetheless
there remains an enthralling challenge to optimize cash flows
associated with synthetic CDOs. A Gaussian-based model is used
here in which default correlation and unconditional probabilities of
default are highlighted. Then numerous simulations are performed
based on this model for different scenarios in order to evaluate the
associated cash flows given a specific number of defaults at different
periods of time. Cash flows are not solely calculated on a single
bought or sold tranche but rather on a combination of bought and
sold tranches. With some assumptions, the simplex algorithm gives
a way to find the maximum cash flow according to correlation of
defaults and maturities. The used Gaussian model is not realistic in
crisis situations. Besides present system does not handle buying or
selling a portion of a tranche but only the whole tranche. However the
work provides the investor with relevant elements on how to know
what and when to buy and sell.