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Valuation of collateralized debt obligations: An equilibrium model

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  • Hu, May
  • Park, Jason

Abstract

In this paper, we present a new equilibrium model for pricing collateralized debt obligations (CDOs). The model is grounded on option pricing theory and features a random jump size to account for default correlation across reference entities. This feature is important for pricing CDOs during times of market turmoil. Simulation results show that jump size volatility, capturing uncertainty about the size of simultaneous corporate defaults, is a key parameter in pricing CDOs. The effect of jump size volatility on CDO spreads is substantial and depends on the relative position of the mean jump size to loss-coverage limits.

Suggested Citation

  • Hu, May & Park, Jason, 2019. "Valuation of collateralized debt obligations: An equilibrium model," Economic Modelling, Elsevier, vol. 82(C), pages 119-135.
    • Handle: RePEc:eee:ecmode:v:82:y:2019:i:c:p:119-135
    DOI: 10.1016/j.econmod.2019.08.014
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    1. Taehan Bae & Ian Iscoe & Changki Kim, 2015. "Valuing Retail Credit Tranches with Structural, Double Mixture Models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 35(9), pages 849-867, September.
    2. Duffee, Gregory R, 1999. "Estimating the Price of Default Risk," The Review of Financial Studies, Society for Financial Studies, vol. 12(1), pages 197-226.
    3. Glasserman, Paul & Suchintabandid, Sira, 2007. "Correlation expansions for CDO pricing," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1375-1398, May.
    4. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-367, May.
    5. X. Burtschell & Jonathan Gregory & Jean-Paul Laurent, 2009. "A Comparative Analysis of CDO Pricing Models under the Factor Copula Framework," Post-Print hal-03676448, HAL.
    6. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    7. Rubinstein, Mark, 1985. "Nonparametric Tests of Alternative Option Pricing Models Using All Reported Trades and Quotes on the 30 Most Active CBOE Option Classes from August 23, 1976 through August 31, 1978," Journal of Finance, American Finance Association, vol. 40(2), pages 455-480, June.
    8. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," The Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    9. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    10. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    11. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    12. Bakshi, Gurdip S. & Zhiwu, Chen, 1997. "An alternative valuation model for contingent claims," Journal of Financial Economics, Elsevier, vol. 44(1), pages 123-165, April.
    13. Amin, Kaushik I & Ng, Victor K, 1993. "Option Valuation with Systematic Stochastic Volatility," Journal of Finance, American Finance Association, vol. 48(3), pages 881-910, July.
    14. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    15. Bakshi, Gurdip S & Chen, Zhiwu, 1997. "Equilibrium Valuation of Foreign Exchange Claims," Journal of Finance, American Finance Association, vol. 52(2), pages 799-826, June.
    16. Louis O. Scott, 1997. "Pricing Stock Options in a Jump‐Diffusion Model with Stochastic Volatility and Interest Rates: Applications of Fourier Inversion Methods," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 413-426, October.
    17. Wiggins, James B., 1987. "Option values under stochastic volatility: Theory and empirical estimates," Journal of Financial Economics, Elsevier, vol. 19(2), pages 351-372, December.
    18. Bailey, Warren & Stulz, René M., 1989. "The Pricing of Stock Index Options in a General Equilibrium Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(1), pages 1-12, March.
    19. John M. Griffin & Dragon Yongjun Tang, 2012. "Did Subjectivity Play a Role in CDO Credit Ratings?," Journal of Finance, American Finance Association, vol. 67(4), pages 1293-1328, August.
    20. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    21. Francis A. Longstaff & Arvind Rajan, 2008. "An Empirical Analysis of the Pricing of Collateralized Debt Obligations," Journal of Finance, American Finance Association, vol. 63(2), pages 529-563, April.
    22. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    23. Philippe Jorion, 1988. "On Jump Processes in the Foreign Exchange and Stock Markets," The Review of Financial Studies, Society for Financial Studies, vol. 1(4), pages 427-445.
    24. Iscoe, Ian & Kreinin, Alexander, 2007. "Valuation of synthetic CDOs," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3357-3376, November.
    25. Joshua D. Coval & Jakub W. Jurek & Erik Stafford, 2009. "Economic Catastrophe Bonds," American Economic Review, American Economic Association, vol. 99(3), pages 628-666, June.
    26. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    27. Joost Driessen, 2005. "Is Default Event Risk Priced in Corporate Bonds?," The Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 165-195.
    28. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    29. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    30. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(4), pages 419-438, December.
    31. Dan Luo & Dragon Yongjun Tang & Sarah Qian Wang, 2018. "Model specification and collateralized debt obligation (mis)pricing," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(11), pages 1284-1312, November.
    32. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    33. Ball, Clifford A & Torous, Walter N, 1985. "On Jumps in Common Stock Prices and Their Impact on Call Option Pricing," Journal of Finance, American Finance Association, vol. 40(1), pages 155-173, March.
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    More about this item

    Keywords

    Collateralized debt obligations; Default correlation; Global financial crisis;
    All these keywords.

    JEL classification:

    • G01 - Financial Economics - - General - - - Financial Crises
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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