Editor: Ashish Dev
Published: 29 Dec 2008
Papers in this issue
by Chulwoo Han, Jangkoo Kang
by JanW. Kwiatkowski
by Alexander Herbertsson
Practice Leader, ERM and Structured Products Advisory, Promontory Financial, New York
During the short period between the publication of the last issue of The Journal of Credit Risk and this issue, the US mortgage-related financial crisis of 2007-08 has progressed into not only a broader financial sector crisis but an even broader economywide recession, not only in the US but probably globally. House prices have seen an unprecedented decline in the US. It is unprecedented because the decline is more or less across the whole of the country.Yet the primary problem of mortgage foreclosures and losses can be boxed. There are numerous predictions.
Whichever prediction is relied on, the realized and potential losses in US mortgage loans is far less than the dollar value of market capitalization that has been eroded not only since October 2007 but in just the past few months. Granted, the crisis was originally catalyzed by delinquency problems in US subprime mortgages, in particular, and potentially in the much larger class of Alt-A mortgages. The packaging of such mortgages as structured credit products and their repackaging as CDOs and synthetic CDOs resulted in huge trading losses in the books of banks and investors throughout the world. But in terms of systemic effects, it now appears that a crisis of confidence, flight to (extreme) quality and a credit crunch in all sectors are as much the causes of the current crisis as mortgage delinquencies are. The overall credit crunch has an interesting angle. Banks, at least the credit underwriting function of banks, have a habit of loosening underwriting standards during the boom of a credit cycle and then tightening underwriting standards during a recession. A bank may ask for and get considerably better collateral and set much stronger covenants today. It can also charge much wider spreads. The overall risk-adjusted return on credit originated after the tightening may very well be higher than the ones originated just before the recession, even though the borrowers' finances are weaker. For example, consider non-agency mortgages. Banks can ask for, say, 30% equity and charge a much higher coupon today, and a portfolio of such mortgages is actually better for a bank than the portfolio of Option ARMs (adjustable rate mortgages with the option to pay less than the interest let alone any principal in the first few years; the borrower has the option) it originated or bought in 2005 or 2006. In many circles, the view is that banks are better off not lending in this environment even after receiving public money as capital infusion. But we cannot simply take this for granted. If anything, the traditional credit culture in banks of closing the stable door after the horse has bolted may have been a major factor in creating the position in which the financial industry now finds itself.
In this issue we present three full-length research papers and one technical report. The first paper, "Pricing synthetic CDO tranches in a model with default contagion using the matrix analytic approach," is by Herbertsson. In this paper, the author values synthetic CDO tranches, kth-to-default swap spreads and tranchelets in an intensity based credit risk model with default contagion. The default intensity of an obligor undergoes a jump at the default of any other obligor in the portfolio. Reinterpreting the formulation as a Markov jump process, the author uses a matrix analytic approach to derive computationally tractable closed-form expressions for the credit derivatives mentioned above. For a fixed maturity of five years, a homogeneous portfolio is calibrated against CDO tranche spreads, index CDS spreads and the average CDS spread, all taken from the iTraxx Europe series. After the calibration, the author computes spreads for tranchelets and kth-to-default swap spreads for different subportfolios of the main portfolio.
The second paper, "On the estimation of credit exposures using regression-based Monte Carlo simulation," is by Schöftner. In this paper, the author provides an application of the regression-based Monte-Carlo simulation approach for modeling the credit exposure of complex products, especially path-dependent derivatives that do not admit the closed-form analytical solution. The technique is based on the method developed by Longstaff and Schwartz to price American options by backward induction. The author approximates the conditional expectation with a relatively small set of simulated scenarios to reduce the number of simulation paths. The modeling approach presented in this paper complements the work by Lomibao and Zhu for cases where the closed-form solution is unattainable.
The third paper, "An extended CreditRiskC framework for portfolio credit risk management," is by Han and Kang. The paper describes an extension, called the common factor model, of the so-called hidden gamma approach of Giese to modeling dependencies between sectors/risk factors in the CreditRiskC framework. The authors then compare this common factor model with the original CreditRiskC model, as well as with Giese's extensions: the hidden gamma model and the compound gamma model. They show that, in a case study of Korean data, the increased degrees of freedom perform much better when fitting the model's covariance structure to an observed one than the "hidden gamma" and "compound gamma" approaches of Giese. The second part of the paper uses simulations from the common factor model employing importance sampling and combines them with the linear programming approach first proposed by Andersson et al to perform a conditional value-at-risk optimization of a credit risk portfolio.
A technical report describes a particular practical technique and lists situations in which it works well and others in which it does not. Such reports provide extremely useful information to practitioners in terms of saving time and avoiding duplication of effort. The contents of technical reports complement the rigorous conceptual and model developments that are presented in research papers and provide a great deal of value to practitioners.
The technical report in this volume is Kwiatkowski's "A technical note on the allocation of risk capital in credit portfolios." In an earlier issue of The Journal of Credit Risk, Kwiatkowski and Burridge published a paper on a methodology for computing and allocating risk capital, defined as the conditional expected shortfall over some threshold percentile of the loss distribution, for portfolios of defaultable exposures. The methodology uses the recursive algorithm, first introduced by Andersen et al, for computing the loss distribution of a portfolio, with stochastic losses given default. The recursion is reversed to compute the contributions of the individual constituents. In general, the computation time is dominated by the latter process. In this technical note, Kwiatkowski shows how, using the same formulation, the computation of the individual contributions (the "allocation") may be considerably accelerated, to the extent that the computation time is dominated by the computation of the loss distribution.
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