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Valuation Of Mortgage Insurance Contracts With Counterparty Default Risk: Reduced-Form Approach

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  • Chang, Chia-Chien

Abstract

In the recent subprime mortgage crisis, which has caused banks and insurance companies to go bankrupt or into acquisition, the lender and insurer have exhibited not only correlated defaults when exposed to common risk factors but also counterparty default risk, which is triggered by mortgage defaults. Given the correlated defaults and the counterparty default risk, we use the reduced-form approach to derive the closed-form formulas of mortgage insurance contracts with premium refunds, annual premiums and upfront premiums. Regardless of the nature of the premium structures, the numerical analysis with parameter calibration demonstrates that both the correlated defaults and the counterparty default risk significantly impact mortgage insurance premiums, particularly in long-term mortgage loans.

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  • Chang, Chia-Chien, 2014. "Valuation Of Mortgage Insurance Contracts With Counterparty Default Risk: Reduced-Form Approach," ASTIN Bulletin, Cambridge University Press, vol. 44(2), pages 303-334, May.
    • Handle: RePEc:cup:astinb:v:44:y:2014:i:02:p:303-334_00
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    1. Jarrow, Robert A. & Turnbull, Stuart M., 2000. "The intersection of market and credit risk," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 271-299, January.
    2. Brown, Jane P. & Song, Haiyan & McGillivray, Alan, 1997. "Forecasting UK house prices: A time varying coefficient approach," Economic Modelling, Elsevier, vol. 14(4), pages 529-548, October.
    3. Duffee, Gregory R, 1999. "Estimating the Price of Default Risk," Review of Financial Studies, Society for Financial Studies, vol. 12(1), pages 197-226.
    4. Schwartz, Eduardo S & Torous, Walter N, 1989. " Prepayment and the Valuation of Mortgage-Backed Securities," Journal of Finance, American Finance Association, vol. 44(2), pages 375-392, June.
    5. Robert A. Jarrow & Fan Yu, 2008. "Counterparty Risk and the Pricing of Defaultable Securities," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 20, pages 481-515, World Scientific Publishing Co. Pte. Ltd..
    6. Yongheng Deng & John M. Quigley & Robert Van Order, 2000. "Mortgage Terminations, Heterogeneity and the Exercise of Mortgage Options," Econometrica, Econometric Society, vol. 68(2), pages 275-308, March.
    7. Chia-Chien Chang & Chou-Wen Wang & Chih-Yuan Yang, 2012. "The Effects of Macroeconomic Factors on Pricing Mortgage Insurance Contracts," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 79(3), pages 867-895, September.
    8. Lambrecht, Bart M & Perraudin, William R M & Satchell, Steven, 2003. "Mortgage Default and Possession under Recourse: A Competing Hazards Approach," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 35(3), pages 425-442, June.
    9. Calem, Paul S. & LaCour-Little, Michael, 2004. "Risk-based capital requirements for mortgage loans," Journal of Banking & Finance, Elsevier, vol. 28(3), pages 647-672, March.
    10. Schwartz, Eduardo S & Torous, Walter N, 1992. "Prepayment, Default, and the Valuation of Mortgage Pass-through Securities," The Journal of Business, University of Chicago Press, vol. 65(2), pages 221-239, April.
    11. Ming‐Chi Chen & Chia‐Chien Chang & Shih‐Kuei Lin & So‐De Shyu, 2010. "Estimation of Housing Price Jump Risks and Their Impact on the Valuation of Mortgage Insurance Contracts," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(2), pages 399-422, June.
    12. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    13. Carl Chiarella & Oh-Kang Kwon, 1999. "Classes of Interest Rate Models Under the HJM Framework," Research Paper Series 13, Quantitative Finance Research Centre, University of Technology, Sydney.
    14. Robert A. Jarrow & Stuart M. Turnbull, 2008. "Pricing Derivatives on Financial Securities Subject to Credit Risk," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 17, pages 377-409, World Scientific Publishing Co. Pte. Ltd..
    15. Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. "Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-430, March.
    16. Quigley, John M & Van Order, Robert, 1995. "Explicit Tests of Contingent Claims Models of Mortgage Default," The Journal of Real Estate Finance and Economics, Springer, vol. 11(2), pages 99-117, September.
    17. James Kau & Donald Keenan, 1999. "Catastrophic Default and Credit Risk for Lending Institutions," Journal of Financial Services Research, Springer;Western Finance Association, vol. 15(2), pages 87-102, March.
    18. Stanton, Richard, 1995. "Rational Prepayment and the Valuation Mortgage-Backed Securities," Review of Financial Studies, Society for Financial Studies, vol. 8(3), pages 677-708.
    19. Stefano Caselli & Stefano Gatti & Francesca Querci, 2008. "The Sensitivity of the Loss Given Default Rate to Systematic Risk: New Empirical Evidence on Bank Loans," Journal of Financial Services Research, Springer;Western Finance Association, vol. 34(1), pages 1-34, August.
    20. Kau, James B. & Keenan, Donald C. & Muller III, Walter J. & Epperson, James F., 1995. "The Valuation at Origination of Fixed-Rate Mortgages with Default and Prepayment," The Journal of Real Estate Finance and Economics, Springer, vol. 11(1), pages 5-36, July.
    21. Chia-Chien Chang & Wei-Yi Huang & So-De Shyu, 2012. "Pricing Mortgage Insurance with Asymmetric Jump Risk and Default Risk: Evidence in the U.S. Housing Market," The Journal of Real Estate Finance and Economics, Springer, vol. 45(4), pages 846-868, November.
    22. Eduardo S. Schwartz & Walter N. Torous, 1993. "Mortgage Prepayment and Default Decisions: A Poisson Regression Approach," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 21(4), pages 431-449, December.
    23. Szu‐Lang Liao & Ming‐Shann Tsai & Shu‐Ling Chiang, 2008. "Closed‐Form Mortgage Valuation Using Reduced‐Form Model," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 36(2), pages 313-347, June.
    24. Kau, James B, et al, 1992. "A Generalized Valuation Model for Fixed-Rate Residential Mortgages," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 24(3), pages 279-299, August.
    25. Gordon W. Crawford & Michael C. Fratantoni, 2003. "Assessing the Forecasting Performance of Regime‐Switching, ARIMA and GARCH Models of House Prices," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 31(2), pages 223-243, June.
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    1. Chang-Chih Chen & Chia-Chien Chang, 2019. "How Big are the Ambiguity-Based Premiums on Mortgage Insurances?," The Journal of Real Estate Finance and Economics, Springer, vol. 58(1), pages 133-157, January.

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