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Default Clustering Risks in Commercial Mortgage-Backed Securities

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Abstract

This paper proposes an intensity-based pricing model with default dependence structure for CMBS bonds. Three features are incorporated into the proposed model. First, default is a Poisson jump process defined by a function of mortgage rating information. Second, property risks are modeled using a high dimensional Brownian motion process that captures both systematic risk and idiosyncratic risk in property value. Third, default dependence structure is built into the extended model. Based on a set of input parameters, we simulate various pricing effects on a hypothetical CMBS using the proposed model structure. The results of the base-line intensity model show that yield spreads on CMBS bonds increase in the recovery rate, but decreases in the hazard rate. Security structured with smaller subordination tranche exposes CMBS bonds to higher default risks. The model predicts that default clustering increases required yield spreads of CMBS bonds. At a 70% recovery rate and a 3% default hazard rate, yield spreads of Junior bonds are expected to increase by 169 basis points when counterparty risks increase by 50%. The results highlight the importance of clustering risks associated with counterparty default when valuing CMBS bonds.

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Notes

  1. The CMBS and underlying mortgages are computed based on CMBS issuances in the US, which were rated by the Fitch (formerly known as the Fitch IBCA and Duff & Phelps Credit Rating Co.) between January 1993 and December 2004.

  2. In a CMBS pricing model that integrates the correlations of pooled mortgages with the prioritization structure, Childs et al. (1996) showed that pooling significantly reduces the required yield spreads of subordinated tranches in CMBS.

  3. Pooling could not remove systematic risks caused by market-wide shocks and economic recessions (Hudson-Wilson and Pappadopoulos 1999).

  4. Empirical studies by Snyderman (1991, 1994), Esaki (2002), Esaki et al (1999) and Snyderman and L’Heureux (2002) on commercial mortgage default showed that the default probability and loss severity on liquidated commercial loans vary with multiple characteristics such as loan origination years, property types, and geographic distribution. The proposed model can incorporate these effects into the valuation of commercial mortgages by calibrating their default hazard rates and recovery rates.

  5. Despite the endogenous choice in LTV ratios, uncertainty on the underlying commercial property value is still believed to play an important role in determining the value of its commercial mortgage due to the guarantee role of the property (Kau et al. 2009).

  6. The definition of the high-dimensional Brownian process of property value is motivated by factor models, which have been widely used to describe the covariance structure of asset returns and predict future returns. See Chan et al. (1998) for a recent review of factor models.

  7. Mei and Lee (1994) show the presence of a real estate factor in asset pricing, and provide evidence that equity REITs and the Russell-NCREIF index are driven by the underlying real estate factor.

  8. See, e.g., Joshi (2003, Chapter 11).

  9. Equation (11) clearly specifies the relationship among the commercial mortgage value, property value and default likelihood. We can derive the commercial mortgage value by solving the equation numerically.

  10. Both O’Rourke et al. (2004, 2005) in Fitch Ratings’ rating report and Snyderman and L’Heureux (2002) in Morgan Stanley’s rating report provide more information on the default losses of CMBS commercial mortgages.

  11. See Bluhm et al. (2003) for a more detailed derivation of this relationship.

  12. Kau et al. (2009) estimate the implied default probabilities of CMBS commercial mortgages using the structural-based pricing model. Due to lack of default information of CMBS commercial mortgages, we are not able to estimate the implied default probabilities of CMBS. However, we use the numerical simulation approach to price the CMBS bonds.

  13. In our numerical analysis, to examine the important implication of the hazard rate for the credit qualities of commercial mortgages we allow the average hazard rate to vary in a wider range from 0.1% to 7%.

  14. In practice, borrowers make mortgage payments to the lenders on monthly basis, while the scheduled coupon payments of CMBS bonds are due annually or semi-annually.

  15. If the balloon payment is lower than the property value at time T, [A i (T) < V i (T)], the individual mortgage value is the same as the end-period boundary condition as in equation (14).

  16. The proposed security structures of 70%:25%:5% and 70%:10%:20% for senior, mezzanine and junior tranches follow the same structures used in the analyses by Childs et al. (1996).

  17. Vandell (1995) focuses on the investigation of the non-ruthless behavior of mortgage obligors, and emphasizes the importance of incorporating the non-ruthless behavior into mortgage pricing models.

  18. Liu et al. (2009) use Copula-based models to evaluate the effect of correlation structure of pooled mortgages on the credit risks of CMBS.

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Acknowledgement

The research funding from National University of Singapore is acknowledged. We are grateful to Fu Yuming, Walter Torous, Brent Ambrose, Daniel Quan, Charles Leung, and participants at the 2005 International Japanese Association of Real Estate Financial Engineering (JAREFE) conference for comments. Any errors remain the sole responsibility of the authors.

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Authors and Affiliations

  1. Department of Real Estate, Konkuk University, 1 Hwayang-dong, Kwangjin-gu, Seoul, Korea, 143–701

    Gang-Zhi Fan

  2. Department of Real Estate School of Design & Environment, National University of Singapore, 4 Architecture Drive, Singapore, 117566, Singapore

    Tien Foo Sing & Seow Eng Ong

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  1. Gang-Zhi Fan
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  2. Tien Foo Sing
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Correspondence to Tien Foo Sing.

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Fan, GZ., Sing, T.F. & Ong, S.E. Default Clustering Risks in Commercial Mortgage-Backed Securities. J Real Estate Finan Econ 45, 110–127 (2012). https://doi.org/10.1007/s11146-011-9315-2

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