, McMaster University
The Affine Markov Chain Model for Credit Risk
The AMC model of credit risk is a natural union of the structural
and intensity based frameworks which combines credit ratings migration
and default with stochastic interest rates and recovery rates. It has
very nice properties: when applied to one or two firms, closed formulas
can be derived for default probabilities, bond prices, and even credit
default swaps, resulting in very efficient computations. After describing
this new approach, I will move on to look at basket derivatives on large
numbers of firms, specifically collateralized debt obligations (CDOs).
The market for such products is now hot, but current CDO pricing technology
does not rest on a coherent consistent model. I will describe how these
products can be priced and hedged very flexibly and efficiently in the
AMC modelling framework.
Joint work with Alexey Kuznetsov
Michael Gordy, US Federal Reserve
Model Foundations for the Treatment of CDOs in Basell II
In its proposal for a New Basel Accord, the Basel Committee on Bank
Supervision (2004, Part 2.IV) offers two methodologies for assigning
regulatory capital charges to securitization exposures under the Internal
Ratings-Based (IRB) approach. The Ratings-Based Approach sets capital
primarily as a function of an external rating, such as might be assigned
by Moody's or S&P, and is to be employed whenever an external rating
is available. As many securitization exposures are not externally rated,
the alternative Supervisory Formula Approach (SFA) determines required
capital as a function of the characteristics of the collateral pool
and contractual properties of the tranche. The chapter sets forth the
theoretical foundation for the SFA provided by the "uncertainty
in loss prioritization" (ULP) model of Gordy and Jones (2003).
Greg M. Gupton, Sr. Director of Research,
Advancing Loss Given Default Prediction Models, Modeling framework,
fitting, and validation
We describe LossCalc version 2: the Moody's KMV model to predict
loss given default (LGD): the equivalent of (1 - recovery rate).
LossCalc is a statistical model that applies multiple predictive factors
at different information levels: collateral, instrument, firm, industry,
country, and the macroeconomy to predict LGD. We find that Distance-to-Default
measures (from the Moodys KMV structual model of default likelihood)
compiled at both the industry and firm levels are predictive of LGD.
We find that recovery rates world-wide are predictable within a common
statistical framework which suggests that estimates of economic firm
value (which is then available to allocate to claimants according to
each coutrys bankruptcy laws) is a dominant step in LGD determination.
LossCalc is built on a global dataset of 3,026 recovery observations
for loans, bonds, and preferred stock from 1981-2004. This dataset includes
1,424 defaults of both public and private firms; both rated and unrate
instruments; in all industries. We demonstrate out-of-sample and out-of-time
LGD model validation. The model significantly improves on the use of
historical recovery averages to predict LGD.
Niall Whelan, Scotia Capital
Quantifying Counterparty Credit Risk
Counterparty credit risk is extremely topical in light of the new
Basel accords on capital adequacy. Minimising capital requirements associated
with derivatives activities requires simulating counterparty portfolios.
This can be very difficult since large financial institutions can have
thousands of counterparties, collectively containing tens of thousands
of transactions and involving dozens of distinct market risk factors.
This is a large software engineering exercise. In this talk I will present
ideas for making this manageable; they stress adaptability and flexibility
while avoiding large-scale Monte-Carlo simulations. Time permitting,
I will discuss other risk management applications, some of which involve
the two-sided nature of credit risk.
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