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Structured Assets

  • Zura Kakushadze
  • Juan Andrés Serur
Chapter

Abstract

This chapter begins by reviewing some pertinent aspects of asset-backed securities (ABS) and collateralized debt obligations (CDOs), including the CDO tranche structure, expected loss, premium and liability legs, spread, mark-to-market, and risky duration. The chapter discusses trading strategies, including detailed mathematical descriptions, based on CDO carry trades involving Delta-hedging a long equity tranche of a CDO with a short CDS index position, Delta-hedging a short senior/mezzanine tranche with a long index position, Delta-hedging a long lower quality tranche with a short higher quality tranche, or Delta-hedging a tranche with a single-name CDS, CDO curve trades such as steepeners and flatteners, including notional-neutral, risky duration-neutral, and carry-neutral trading strategies, and mortgage-back security (MBS) trading strategies, which deal with the mortgage prepayment risk.

Keywords

Asset-backed security (ABS) Collateralized debt obligation (CDO) CDO tranche Expected loss Premium leg Liability leg CDO spread Mark-to-market Risky duration CDO carry trades Delta-hedging CDS index Single-name CDS CDO curve trades Steepener Flattener Mortgage-back security (MBS) Attachment point Detachment point CDO notional Reference entities Delta Index hedging MBS passthrough Prepayment risk 

References

  1. Aït-Sahalia, Y., & Duarte, J. (2003). Nonparametric Option Pricing Under Shape Restrictions. Journal of Econometrics, 116(1–2), 9–47.CrossRefGoogle Scholar
  2. Altman, E. I., Brady, B., Resti, A., & Sironi, A. (2005). The Link Between Default and Recovery Rates: Theory, Empirical Evidence and Implications. Journal of Business, 78(6), 2203–2228.CrossRefGoogle Scholar
  3. Amato, J. D., & Gyntelberg, J. (2005, December). CDS Index Tranches and the Pricing of Credit Risk Correlations. BIS Quarterly Review, pp. 73–87. Available online: https://www.bis.org/publ/qtrpdf/r_qt0503g.pdf.
  4. Amato, J. D., & Remolona, E. M. (2003, December). The Credit Spread Puzzle. BIS Quarterly Review, pp. 51–63. Available online: https://www.bis.org/publ/qtrpdf/r_qt0312e.pdf.
  5. Ambrose, B., LaCour-Little, M., & Sanders, A. (2004). The Effect of Conforming Loan Status on Mortgage Yield Spreads: A Loan Level Analysis. Real Estate Economics, 32(4), 541–569.CrossRefGoogle Scholar
  6. Andersen, L., & Sidenius, J. (2005). Extensions to the Gaussian Copula: Random Recovery and Random Factor Loadings. Journal of Credit Risk, 1(1), 29–70.CrossRefGoogle Scholar
  7. Andersen, L., Sidenius, J., & Basu, S. (2003, November). All Your Hedges in One Basket. Risk, pp. 67–72.Google Scholar
  8. Arnsdorf, M., & Halperin, I. (2007). BSLP: Markovian Bivariate Spread-Loss Model for Portfolio Credit Derivatives (Working Paper). Available online: https://arxiv.org/pdf/0901.3398.
  9. Belkin, B., Suchover, S., & Forest, L. (1998). A One-Parameter Representation of Credit Risk and Transition Matrices. Credit Metrics Monitor, 1(3), 46–56.Google Scholar
  10. Biby, J. D., Modukuri, S., & Hargrave, B. (2001). Collateralized Borrowing via Dollar Rolls. In F. J. Fabozzi (Ed.), The Handbook of Mortgage-Backed Securities (5th ed.). New York, NY: McGraw-Hill.Google Scholar
  11. Bielecki, T. R., Brigo, D., & Patras, F. (2011). Credit Risk Frontiers: Subprime Crisis, Pricing and Hedging, CVA, MBS, Ratings, and Liquidity. Hoboken, NJ: Wiley.CrossRefGoogle Scholar
  12. Bielecki, T., Jeanblanc, M., & Rutkowski, M. (2007). Hedging of Basket Credit Derivatives in the Credit Default Swap Market. Journal of Credit Risk, 3(1), 91–132.CrossRefGoogle Scholar
  13. Bielecki, T., Vidozzi, A., & Vidozzi, L. (2008). A Markov Copulae Approach to Pricing and Hedging of Credit Index Derivatives and Ratings Triggered Step-Up Bonds. Journal of Credit Risk, 4(1), 47–76.CrossRefGoogle Scholar
  14. Bobey, B. (2010). The Effects of Default Correlation on Corporate Bond Credit Spreads (Working Paper). Available online: https://ssrn.com/abstract=1510170.
  15. Bol, G., Rachev, S. T., & Würth, R. (Eds.). (2009). Risk Assessment: Decisions in Banking and Finance. Heidelberg, Germany: Physica-Verlag.Google Scholar
  16. Boscher, H., & Ward, I. (2002, June). Long or Short in CDOs. Risk, pp. 125–129.Google Scholar
  17. Boudoukh, J., Whitelaw, R., Richardson, M., & Stanton, R. (1997). Pricing Mortgage-Backed Securities in a Multifactor Interest Rate Environment: A Multivariate Density Estimation Approach. Review of Financial Studies, 10(2), 405–446.CrossRefGoogle Scholar
  18. Brazil, A. J. (1988). Citicorp’s Mortgage Valuation Model: Option-Adjusted Spreads and Option-Based Durations. Journal of Real Estate Finance and Economics, 1(2), 151–162.CrossRefGoogle Scholar
  19. Brennan, M. J., & Schwartz, E. S. (1985). Determinants of GNMA Mortgage Prices. Real Estate Economics, 13(3), 209–228.CrossRefGoogle Scholar
  20. Burtshell, X., Gregory, J., & Laurent, J.-P. (2009). A Comparative Analysis of CDO Pricing Models Under the Factor Copula Framework. Journal of Derivatives, 16(4), 9–37.CrossRefGoogle Scholar
  21. Carmona, R., & Crépey, S. (2010). Particle Methods for the Estimation of Credit Portfolio Loss Distributions. International Journal of Theoretical and Applied Finance, 13(4), 577–602.CrossRefGoogle Scholar
  22. Carron, A. S., & Hogan, M. (1988). The Option Valuation Approach to Mortgage Pricing. Journal of Real Estate Finance and Economics, 1(2), 131–149.CrossRefGoogle Scholar
  23. Chinloy, P. (1989). The Probability of Prepayment. Journal of Real Estate Finance and Economics, 2(4), 267–283.CrossRefGoogle Scholar
  24. Choroś-Tomczyk, B., Härdle, W. K., & Okhrin, O. (2016). A Semiparametric Factor Model for CDO Surfaces Dynamics. Journal of Multivariate Analysis, 146, 151–163.CrossRefGoogle Scholar
  25. Cont, R., & Minca, A. (2013). Recovering Portfolio Default Intensities Implied by CDO Quotes. Mathematical Finance, 23(1), 94–121.CrossRefGoogle Scholar
  26. Cousin, A., & Laurent, J. (2012). Dynamic Hedging of Synthetic CDO Tranches: Bridging the Gap Between Theory and Practice. In T. R. Bielecki, D. Brigo, & F. Patras (Eds.), Credit Risk Frontiers (Chapter 6). Hoboken, NJ: Wiley.CrossRefGoogle Scholar
  27. Crabbe, L. E., & Fabozzi, F. J. (2002). Corporate Bond Portfolio Management. Hoboken, NJ: Wiley.Google Scholar
  28. Das, S. (2005). Credit Derivatives: Trading & Management of Credit & Default Risk (3rd ed.). Hoboken, NJ: Wiley.Google Scholar
  29. Davidson, A. S., Herskovitz, M. D., & Van Drunen, L. D. (1988). The Refinancing Threshold Pricing Model: An Economic Approach to Valuing MBS. Journal of Real Estate Finance and Economics, 1(2), 117–130.CrossRefGoogle Scholar
  30. Davis, M., & Lo, V. (2001). Infectious Defaults. Quantitative Finance, 1(4), 382–387.CrossRefGoogle Scholar
  31. Dechario, T., Mosser, P., Tracy, J., Vickery, J., & Wright, J. (2010). A Private Lender Cooperative Model for Residential Mortgage Finance (Federal Reserve Bank of New York Staff Reports, No. 466). Available online: https://www.newyorkfed.org/medialibrary/media/research/staff_reports/sr466.pdf.
  32. Detlefsen, K., & Härdle, W. K. (2013). Variance Swap Dynamics. Quantitative Finance, 13(5), 675–685.CrossRefGoogle Scholar
  33. Ding, J. J., & Sherris, M. (2011). Comparison of Market Models for Measuring and Hedging Synthetic CDO Tranche Spread Risks. European Actuarial Journal, 1(S2), 261–281.CrossRefGoogle Scholar
  34. Douglas, R. (Ed.). (2007). Credit Derivative Strategies: New Thinking on Managing Risk and Return. New York, NY: Bloomberg Press.Google Scholar
  35. Downing, C., Jaffee, D., & Wallace, N. (2009). Is the Market for Mortgage-Backed Securities a Market for Lemons? Review of Financial Studies, 22(7), 2457–2494.CrossRefGoogle Scholar
  36. Duarte, J., Longstaff, F. A., & Yu, F. (2006). Risk and Return in Fixed-Income Arbitrage: Nickels in Front of a Steamroller? Review of Financial Studies, 20(3), 769–811.CrossRefGoogle Scholar
  37. Duffie, D. (2004, April). Time to Adapt Copula Methods for Modelling Credit Risk Correlation. Risk, p. 77.Google Scholar
  38. Duffie, D., & Gârleanu, N. (2001). Risk and Valuation of Collateralized Debt Obligations. Financial Analysts Journal, 57(1), 41–59.CrossRefGoogle Scholar
  39. Duffie, D., & Huang, M. (1996). Swap Rates and Credit Quality. Journal of Finance, 51(2), 921–949.CrossRefGoogle Scholar
  40. Duffie, D., & Singleton, K. J. (1997a). Modeling Term Structures of Defaultable Bonds. Review of Financial Studies, 12(4), 687–720.CrossRefGoogle Scholar
  41. Duffie, D., & Singleton, K. J. (1997b). An Econometric Model of the Term Structure of Interest Rate Swap Yields. Journal of Finance, 52(4), 1287–1321.CrossRefGoogle Scholar
  42. Dunn, K. B., & McConnell, J. J. (1981a). A Comparison of Alternative Models for Pricing GNMA Mortgage-Backed Securities. Journal of Finance, 36(2), 471–484.CrossRefGoogle Scholar
  43. Dunn, K. B., & McConnell, J. J. (1981b). Valuation of GNMA Mortgage-Backed Securities. Journal of Finance, 36(3), 599–616.CrossRefGoogle Scholar
  44. Dynkin, L., Hyman, J., Konstantinovsky, V., & Roth, N. (2001). Building an MBS Index: Conventions and Calculations. In F. J. Fabozzi (Ed.), The Handbook of Mortgage-Backed Securities (5th ed.). New York, NY: McGraw-Hill.Google Scholar
  45. Fabozzi, F. J. (2006a). Fixed Income Mathematics: Analytical & Statistical Techniques. New York, NY: McGraw-Hill.Google Scholar
  46. Fabozzi, F. J. (Ed.). (2006b). The Handbook of Mortgage-Backed Securities. New York, NY: McGraw-Hill.Google Scholar
  47. Finger, C. C. (1999). Conditional Approaches for Credit Metrics Portfolio Distributions. Credit Metrics Monitor, 2(1), 14–33.Google Scholar
  48. Frey, R., McNeil, A., & Nyfeler, N. (2001, October). Copulas and Credit Models. Risk, pp. 111–114.Google Scholar
  49. Frey, R., & Backhaus, J. (2008). Pricing and Hedging of Portfolio Credit Derivatives with Interacting Default Intensities. International Journal of Theoretical and Applied Finance, 11(6), 611–634.CrossRefGoogle Scholar
  50. Frey, R., & Backhaus, J. (2010). Dynamic Hedging of Synthetic CDO Tranches with Spread Risk and Default Contagion. Journal of Economic Dynamics and Control, 34(4), 710–724.CrossRefGoogle Scholar
  51. Gabaix, X., Krishnamurthy, A., & Vigneron, O. (2007). Limits of Arbitrage: Theory and Evidence from the Mortgage-Backed Securities Market. Journal of Finance, 62(2), 557–595.CrossRefGoogle Scholar
  52. Gibson, M. S. (2004). Understanding the Risk of Synthetic CDOs (Finance and Economics Discussion Series (FEDS), Paper No. 2004-36). Washington, DC: Board of Governors of the Federal Reserve System. Available online: https://www.federalreserve.gov/pubs/feds/2004/200436/200436pap.pdf.
  53. Giesecke, K., & Weber, S. (2006). Credit Contagion and Aggregate Losses. Journal of Economic Dynamics and Control, 30(5), 741–767.CrossRefGoogle Scholar
  54. Glaeser, E. L., & Kallal, H. D. (1997). Thin Markets, Asymmetric Information, and Mortgage-Backed Securities. Journal of Financial Intermediation, 6(1), 64–86.CrossRefGoogle Scholar
  55. Goodman, L. S. (2002). Synthetic CDOs: An Introduction. Journal of Derivatives, 9(3), 60–72.CrossRefGoogle Scholar
  56. Goodman, L. S., & Lucas, D. J. (2002). And When CDOs PIK? Journal of Fixed Income, 12(1), 96–102.CrossRefGoogle Scholar
  57. Hagenstein, F., Mertz, A., & Seifert, J. (2004). Investing in Corporate Bonds and Credit Risk. London, UK: Palgrave Macmillan.CrossRefGoogle Scholar
  58. Hamerle, A., Igl, A., & Plank, K. (2012). Correlation Smile, Volatility Skew, and Systematic Risk Sensitivity of Tranches. Journal of Derivatives, 19(3), 8–27.CrossRefGoogle Scholar
  59. Herbertsson, A. (2008). Pricing Synthetic CDO Tranches in a Model with Default Contagion Using the Matrix-Analytic Approach. Journal of Credit Risk, 4(4), 3–35.CrossRefGoogle Scholar
  60. Houdain, J. P., & Guegan, D. (2006). Hedging Tranches Index Products: Illustration of Model Dependency. ICFAI Journal of Derivatives Markets, 4, 39–61.Google Scholar
  61. Hu, J. (2001). Basics of Mortgage-Backed Securities (2nd ed.). Hoboken, NJ: Wiley.Google Scholar
  62. Hull, J. C., & White, A. D. (2004). Valuation of a CDO and an \(n\)th to Default CDS Without Monte Carlo Simulation. Journal of Derivatives, 12(2), 8–23.CrossRefGoogle Scholar
  63. Hull, J. C., & White, A. D. (2006). Valuing Credit Derivatives Using an Implied Copula Approach. Journal of Derivatives, 14(2), 8–28.CrossRefGoogle Scholar
  64. Hull, J. C., & White, A. D. (2010). An Improved Implied Copula Model and Its Application to the Valuation of Bespoke CDO Tranches. Journal of Investment Management, 8(3), 11–31.Google Scholar
  65. Jarrow, R., Lando, D., & Turnbull, S. (1997). A Markov Model for the Term Structure of Credit Spreads. Review of Financial Studies, 10(2), 481–523.CrossRefGoogle Scholar
  66. Jarrow, R. A., & Turnbull, S. M. (1995). Pricing Derivatives on Financial Securities Subject to Credit Risk. Journal of Finance, 50(1), 53–85.CrossRefGoogle Scholar
  67. Jobst, A. (2005). Tranche Pricing in Subordinated Loan Securitization. Journal of Structured Finance, 11(2), 64–96.CrossRefGoogle Scholar
  68. Jobst, A. (2006a). European Securitization: A GARCH Model of Secondary Market Spreads. Journal of Structured Finance, 12(1), 55–80.CrossRefGoogle Scholar
  69. Jobst, A. (2006b). Sovereign Securitization in Emerging Markets. Journal of Structured Finance, 12(3), 2–13.CrossRefGoogle Scholar
  70. Jobst, A. (2006c). Correlation, Price Discovery and Co-movement of ABS and Equity. Derivatives Use, Trading & Regulation, 12(1–2), 60–101.CrossRefGoogle Scholar
  71. Jobst, A. (2007). A Primer on Structured Finance. Journal of Derivatives & Hedge Funds, 13(3), 199–213.CrossRefGoogle Scholar
  72. Kakodkar, A., Galiani, S., Jónsson, J. G., & Gallo, A. (2006). Credit Derivatives Handbook 2006—Vol. 2: A Guide to the Exotics Credit Derivatives Market. New York, NY: Credit Derivatives Strategy, Merrill Lynch.Google Scholar
  73. Kau, J. B., Keenan, D. C., Muller, W. J., & Epperson, J. F. (1995). The Valuation at Origination of Fixed-Rate Mortgages with Default and Prepayment. Journal of Real Estate Finance and Economics, 11(1), 5–36.CrossRefGoogle Scholar
  74. Koopman, S. J., Lucas, A., & Schwaab, B. (2012). Dynamic Factor Models with Macro, Frailty, and Industry Effects for U.S. Default Counts: The Credit Crisis of 2008. Econometric Reviews, 30(4), 521–532.CrossRefGoogle Scholar
  75. Laurent, J.-P., Cousin, A., & Fermanian, J. D. (2011). Hedging Default Risks of CDOs in Markovian Contagion Models. Quantitative Finance, 11(12), 1773–1791.CrossRefGoogle Scholar
  76. Laurent, J.-P., & Gregory, J. (2005). Basket Default Swaps, CDOs and Factor Copulas. Journal of Risk, 7(4), 8–23.CrossRefGoogle Scholar
  77. Li, D. X. (2000). On Default Correlation: A Copula Function Approach. Journal of Fixed Income, 9(4), 43–54.CrossRefGoogle Scholar
  78. Lin, S.-Y., & Shyy, G. (2008). Credit Spreads, Default Correlations and CDO Tranching: New Evidence from CDS Quotes (Working Paper). Available online: https://ssrn.com/abstract=496225.
  79. Longstaff, F. (2005). Borrower Credit and the Valuation of Mortgage-Backed Securities. Real Estate Economics, 33(4), 619–661.CrossRefGoogle Scholar
  80. Lucas, D. J., Goodman, L. S., & Fabozzi, F. J. (Eds.). (2006). Collateralized Debt Obligations: Structures and Analysis. Hoboken, NJ: Wiley.Google Scholar
  81. McConnell, J. J., & Buser, S. A. (2011). The Origins and Evolution of the Market for Mortgage-Backed Securities. Annual Review of Financial Economics, 3, 173–192.CrossRefGoogle Scholar
  82. McKenzie, J. A. (2002). A Reconsideration of the Jumbo/Non-Jumbo Mortgage Rate Differential. Journal of Real Estate Finance and Economics, 25(2–3), 197–213.CrossRefGoogle Scholar
  83. Meissner, G. (Ed.). (2008). The Definitive Guide to CDOs. London, UK: Incisive Media.Google Scholar
  84. Nothaft, F. E., Lekkas, V., & Wang, G. H. K. (1995). The Failure of the Mortgage-Backed Futures Contract. Journal of Futures Markets, 15(5), 585–603.CrossRefGoogle Scholar
  85. Packer, F., & Zhu, H. (2005, March). Contractual Terms and CDS Pricing. BIS Quarterly Review, pp. 89–100. Available online: https://www.bis.org/publ/qtrpdf/r_qt0503h.pdf.
  86. Passmore, W., Sherlund, S. M., & Burgess, G. (2005). The Effect of Housing Government-Sponsored Enterprises on Mortgage Rates. Real Estate Economics, 33(3), 427–463.CrossRefGoogle Scholar
  87. Prince, J. T. (2005). Investing in Collateralized Debt Obligations. In CFA Institute Conference Proceedings (Vol. 2005, No. 1, pp. 52–61).CrossRefGoogle Scholar
  88. Rajan, A., McDermott, G., & Roy, R. (Eds.). (2007). The Structured Credit Handbook. Hoboken, NJ: Wiley.Google Scholar
  89. Richard, S. F., & Roll, R. (1989). Prepayments on Fixed-Rate Mortgage-Backed Securities. Journal of Portfolio Management, 15(3), 73–82.CrossRefGoogle Scholar
  90. Schmidt, W., & Ward, I. (2002, January). Pricing Default Baskets. Risk, pp. 111–114.Google Scholar
  91. Schönbucher, P. J. (2003). Credit Derivatives Pricing Models. Hoboken, NJ: Wiley.Google Scholar
  92. Schultz, G. M. (2016). Investing in Mortgage-Backed and Asset-Backed Securities: Financial Modeling with R and Open Source Analytics + Website. Hoboken, NJ: Wiley.Google Scholar
  93. Schwartz, E. S., & Torous, W. N. (1989). Prepayment and the Valuation of Mortgage-Backed Securities. Journal of Finance, 44(2), 375–392.CrossRefGoogle Scholar
  94. Schwartz, E. S., & Torous, W. N. (1992). Prepayment, Default, and the Valuation of Mortgage Pass-Through Securities. Journal of Business, 65(2), 221–239.CrossRefGoogle Scholar
  95. Stanton, R. (1995). Rational Prepayment and the Valuation of Mortgage-Backed Securities. Review of Financial Studies, 8(3), 677–708.CrossRefGoogle Scholar
  96. Tavakoli, J. M. (1998). Credit Derivatives & Synthetic Structures: A Guide to Instruments and Applications (2nd ed.). Hoboken, NJ: Wiley.Google Scholar
  97. Thibodeau, T. G., & Giliberto, S. M. (1989). Modeling Conventional Residential Mortgage Refinancing. Journal of Real Estate Finance and Economics, 2(4), 285–299.Google Scholar
  98. Vasicek, O. A. (2015). Probability of Loss on Loan Portfolio. In O. A. Vasicek (Ed.), Finance, Economics and Mathematics (Chapter 17). Hoboken, NJ: Wiley.Google Scholar
  99. Vickery, J., & Wright, J. (2010). TBA Trading and Liquidity in the Agency MBS Market (Federal Reserve Bank of New York Staff Reports, No. 468). Available online: https://www.newyorkfed.org/medialibrary/media/research/staff_reports/sr468.pdf.
  100. Walker, M. B. (2008). The Static Hedging of CDO Tranche Correlation Risk. International Journal of Computer Mathematics, 86(6), 940–954.CrossRefGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Zura Kakushadze
    • 1
  • Juan Andrés Serur
    • 2
  1. 1.Quantigic Solutions LLCStamfordUSA
  2. 2.Universidad del CEMABuenos AiresArgentina

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