# Journal of Credit Risk

#### Editor's Letter

Ashish Dev

The significant rise in delinquencies and foreclosures that started in the US residential mortgage sector in late 2006 and the effect that rise had on the valuation of structured products that were created out of such residential mortgage loans ended up creating the global economic recession that we are currently in. A somewhat similar crisis is developing in the US commercial mortgage sector. To be sure, the scale is rather different. The US residential mortgage sector is worth about US$11 trillion while the US commercial mortgage sector is worth about US$3.5 trillion. However, to put matters in perspective, the total value of outstanding US commercial mortgage loans has more than tripled in the last decade or so.

Of the US$3.5 trillion, only about US$700 billion has been securitized into commercial mortgage backed securities (CMBSs). Commercial banks in the US hold almost US$2 trillion of commercial real estate loans on their books. Unlike the US residential mortgage market, where only a few large banks hold mortgage loans on their balance sheets, a significant portion of the assets of thousands of community banks in the US is in commercial real estate. Some of them have commercial real estate exposure that exceeds 300% of their total capital. Taking a ratio of exposure to capital (namely, the leverage ratio, which has been a constant impediment to Basel II) is hardly a good measure of risk. But it quickly provides a rough picture of how pervasive the commercial real estate problem can be among community banks. As a consequence, the possible number of bank failures (not the total sum of money involved) and the demand on the Federal Deposit Insurance Corporation could be dramatic. Not all commercial mortgages have similar credit risk characteristics. Typically, bank balance sheets break these loans up into four categories: property loans secured by farms; loans secured by “multifamily” properties, such as apartment buildings or condominiums; construction and land development loans, which are used to acquire land and build newcommercial structures; and non-farm, non-residential loans, which are often associated with already-constructed industrial and office buildings. The delinquency rates in the US for all categories of commercial real estate were negligible only a year ago. By year-end 2008, the rate went up to about 2.5%. Since then, property values have collapsed more than home prices (commercial mortgages are, however, underwritten with much larger possible movement in property prices than are residential mortgages, so this is not a surprise) and vacancy rates are soaring as the recession wears on in the US. The delinquency rate for the construction loan category of commercial real estate had already reached about 12% by year-end 2008. One big difference between residential mortgages and commercial mortgages poses an especially difficult problem for the latter category. Many commercial mortgages amortize only a portion of the principal and therefore require a balloon payment at maturity. This necessitates either a refinancing at maturity or delivery of the remaining principal. Between 2009 and 2012, more than US$1 trillion US commercial real estate loans are expected to mature and will need refinancing. With much tighter underwriting by banks, the cap rates at which refinancing will be available are going to be much higher than those for the current loans.With lower potential income or current net operating income owing to significantly lower occupancy rates in a continuing recession, some of the refinancing will be too expensive, leading to default.

As an asset class, commercial real estate loans exhibit high correlation between the probability of default and the loss given default (PD–LGD correlation) compared with other asset classes. This is because both the propensity to default and the resultant severity of default are dependent on the same commercial building or development. This is especially so in the construction and land development loan category. All else being equal, a higher PD–LGD correlation results in the loss distribution having a fatter tail.

In the end, the macro driver of losses in commercial real estate is how strongly oversupply and recession coincide in terms of time and geography. Owing to more discipline in underwriting aided by better data availability from service providers, the extent of oversupply, as a whole, does not appear to be as severe as in the late 1980s and early 1990s, before the advent of CMBSs. Of course, oversupply is a relative term and also depends on the severity of the recession, which it is still too early to gauge. In this issue we present four full-length research papers and one technical report. The first paper, “Valuing CDOs of bespoke portfolios with implied multi-factor models”, by Rosen and Saunders is on the pricing of bespoke CDOs. The authors address three different types of “bespoke” characteristics: first, where the underlying portfolio and maturity are the same as the reference, but the tranche attachment and/or detachment points are different; second, where the underlying portfolio is the same but the maturity of the portfolio is different from that of observed references; and third, where the underlying portfolio differs from the reference. The model presented is, conceptually, an extension of the implied copula methodology of Hull and White (2006). The authors’CDO valuation framework is based on the application of multifactor credit models in conjunction with weighted Monte Carlo techniques.

In the second paper, “On pricing risky loans and collateralized fund obligations”, by Eberlein et al, the authors derive loan pricing formulas in a Merton-type framework, where the asset value is specified as a process introduced in Carr et al (2007), with negative jumps, that is superposed by a diffusion component. Default is monitored either only at maturity or continuously; the latter assumption requires the non-trivial inversion of the Laplace transform of the distribution of the running minimum of the asset-value process. The model is applied to the pricing of loans and parameter sensitivities, as well as activity rates, are investigated. The model is also calibrated to real data (from General Motors).

The third paper, “Pricing kth-to-default swaps in aLévy-time framework”, is by Mai and Scherer. The paper presents a multivariate credit risk model where dependence on individual default events is incorporated via a stochastic time change. The model is illustrated by the pricing of kth-to-default swaps. The attractive feature of the model is the fact that despite the freedom in specifying the term structures of individual default probabilities, closed-form solutions for the resulting portfolio loss distribution are available. The model can be applied to simultaneously explain individual credit default swap spreads and kth-to-default swap spreads. The dependence structure introduced is thoroughly investigated in the derivations.

In the fourth paper, “CDO pricing with expected loss parametric interpolation”, by Bernis, synthetic CDO transactions are priced based on a polynomial interpolation of the expected loss. This interpolation is done via a polynomial of degree 4 with one additional parameter. The objective is to overcome the incoherence observed when using direct interpolation of base correlations. In practice, many methods for performing such interpolations are ad hoc, and as such do not always preserve regularity or arbitrage conditions. One approach to this problem is to define a single distribution for the tranche loss that recovers all observed prices. In this paper, the author takes a different approach, examining the mapping function from attachment point to expected tranche loss, and establishing required regularity for this mapping. By defining an interpolation method that preserves the needed regularity, the author then guarantees that his interpolated bespoke tranche prices display the desired behavior. The proposed method is compared numerically with other standard methods (base correlation interpolation and random factor loading) on one specific day.

The last paper in this issue is a technical report. A technical report describes a particular practical technique and enumerates situations in which it works well and others in which it does not. Such reports provide extremely useful information to practitioners in terms of saved time and duplication of effort. The contents of technical reports complement the rigorous conceptual and model developments that are presented in the research papers and provide a lot of value for practitioners.

The technical report in this issue, “Double-t copula pricing of structured credit products: practical aspects of a trustworthy implementation”, by Vrins deals with the details of implementing the double-t copula model. The standard one-factor Gaussian copula is commonly used in the industry, but by the very nature of its Gaussian distributional assumption, it suffers from some deficiencies relating to tail behavior: essentially insensitivity of tail dependence to model correlation. The double-t copula was a model proposed by Hull and White (2004) and in different forms by several other researchers. The double-t copula model avoids the undesirable “too light a tail” of the normal copula and fits market prices, especially in recent times, much better than the Gaussian copula does. Intricacies of implementation naturally become more and more important as we go from the much more tractable normal copula to any other specification. As Hull and White will happily admit, their article glossed over some of the technical details in implementing the double-t copula. This article provides the details of an efficient implementation.

REFERENCES

Hull, J., and White, A. (2004).Valuation of a CDO and an n-th to default CDS without Monte Carlo simulation. Journal of Derivatives 12(2), 8–23. Hull, J., and White, A. (2006).Valuing credit derivatives using an implied copula approach. Journal of Derivatives 14(2), 8–28. Carr, P., Geman, H., Madan, D. B., and Yor, M. (2007). Self decomposability and option pricing. Mathematical Finance 17, 31–57.

#### Papers in this issue

##### Double-t copula pricing of structured credit products: practical aspects of a trustworthy implementation

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