Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-13T05:55:12.225Z Has data issue: false hasContentIssue false
  • English
  • Français

VALUATION OF MORTGAGE INSURANCE CONTRACTS WITH COUNTERPARTY DEFAULT RISK: REDUCED-FORM APPROACH

Published online by Cambridge University Press:  11 March 2014

Chia-Chien Chang
Chia-Chien Chang*
Affiliation:
Department of Finance, National Kaohsiung University of Applied Science and RIRC, NCCU, Taipei, Taiwan. Phone: +886-7-3814526
*
E-mail: cchiac@kuas.edu.tw
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

Correlated defaultscounterparty default riskreduced-form modelmortgage insurance premium structures
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 44 , Issue 2 , May 2014 , pp. 303 - 334
Copyright
Copyright © ASTIN Bulletin 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bardhan, A., Karapandza, R. and Urosevic, B. (2006) Valuing mortgage insurance contracts in emerging market economies. The Journal of Real Estate Finance and Economics, 32, 9–20.Google Scholar
Blake, D., Cairns, A.J. and Dowd, K. (2006) Pricing death: Frameworks for the valuation and securitization of mortality risk. ASTIN Bulletin, 36, 79–120.Google Scholar
Brown, J.P., Song, H. and McGillivray, A. (1997) Forecasting U.K. house prices: A time varying coefficient approach. Economic Modeling, 14, 529–548.Google Scholar
Calem, P.S. and LaCour-Little, M. (2004) Risk-based requirements for mortgage loans. Journal of Banking and Finance, 28, 647–672.CrossRefGoogle Scholar
Canner, G.B. and Passmore, W. (1994) Private mortgage insurance. Federal Reserve Bulletin, 9, 883–899.Google Scholar
Caselli, S., Gatti, S. and Querci, F. (2008) The sensitivity of the loss given default rate to systematic risk: New empirical evidence on bank loans. Journal of Financial Services Research, 34, 1–34.Google Scholar
Chang, C.-C., Huang, W.-Y. and Shyu, D. (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, 45 (3), 846–868.Google Scholar
Chang, C.-C., Wang, C.-W. and Yang, C.-Y. (2012) The effects of macroeconomic factors on pricing mortgage insurance contracts. Journal of Risk and Insurance, 79 (3), 867–895.CrossRefGoogle Scholar
Chen, M.C., Chang, C.-C., Lin, S.K. and Shyu, D. (2010) Estimation of housing price jump risks and their impact on the valuation of mortgage insurance contracts. Journal of Risk and Insurance, 77 (2), 399–422.Google Scholar
Chiarella, C. and Kwon, O.K. (2001) Classes of interest rate models under the HJM framework. Asia-Pacific Financial Markets, 8, 1–22.CrossRefGoogle Scholar
Crawford, G. and Fratantoni, M. (2003) Assessing the forecasting performance of regime-switching, ARIMA and GARCH models of house prices. Real Estate Economics, 31 (2), 223–243.Google Scholar
Dahl, M. (2004) Stochastic mortality in life insurance: Market reserves and mortality-linked insurance contracts. Insurance: Mathematics and Economics, 35, 113–136.Google Scholar
Deng, Y. and Quigley, J.M. (2002) Woodhead behavior and the pricing of residential mortgages, Working Paper 2003-1005, University of Southern California, Los Angeles.Google Scholar
Deng, Y., Quigley, J.M. and Van Order, R. (2000) Mortgage terminations, heterogeneity and the exercise of mortgage options. Econometrica, 68, 275–307.Google Scholar
Dennis, B., Kuo, C. and Yang, T. (1997) Rationales of mortgage insurance premium structures. Journal of Real Estate Research, 14 (3), 359–378.Google Scholar
Duffee, G.R. (1999) Estimating the price default risk. The Review of Financial Studies, 12, 197–226.CrossRefGoogle Scholar
Heath, D.C., Jarrow, R.A. and Morton, A.J. (1992) Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation. Econometrica, 60, 77–105.CrossRefGoogle Scholar
Hull, J. and White, A. (1990) Pricing interest rate derivative securities. Review of Financial Studies, 4, 57–392.Google Scholar
Jarrow, R.A. and Turnbull, S.M. (1995) Pricing derivatives on financial securities subject to credit risk. Journal of Finance, 50, 3–85.Google Scholar
Jarrow, R.A. and Turnbull, S.M. (1997) When swaps are dropped. Risk, 10 (5), 70–75.Google Scholar
Jarrow, R.A. and Turnbull, S.M. (2000) The intersection of market and credit risk. Journal of Banking and Finance, 24, 271–299.CrossRefGoogle Scholar
Jarrow, R.A. and Yu, F. (2001) Counterparty risk and the pricing of defaultable securities. Journal of Finance, 56, 1765–1800.CrossRefGoogle Scholar
Kau, J. and Keenan, D. (1995) An overview of the option-theoretic pricing of mortgages. Journal of Housing Research, 6 (2), 217–244.Google Scholar
Kau, J. and Keenan, D. (1999) Catastrophic default and credit risk for lending institutions. Journal of Financial Services Research, 15 (2), 87–102.Google Scholar
Kau, J., Keenan, D., Muller, W. and Epperson, J. (1992) A generalized valuation model for fixed-rate residential mortgages. Journal of Money, Credit and Banking, 24, 280–299.CrossRefGoogle Scholar
Kau, J., Keenan, D. and Muller, W. (1993) An option-based pricing model of private mortgage insurance. The Journal of Risk and Insurance, 60 (2), 288–299.Google Scholar
Kau, J., Keenan, D., Muller, W. and Epperson, J. (1995) The valuation at origination of fixed-rate mortgages with default and prepayment. The Journal of Real Estate Finance and Economics, 11 (1), 5–36.Google Scholar
Lambrecht, B., Perraudin, W. and Satchell, S. (2003) Mortgage default and possession under recourse: a competing hazards approach. Journal of Money, Credit, and Banking, 35 (3), 425–442.Google Scholar
Liao, S.L., Tsai, M.S. and Chiang, S.L. (2008) Closed-form mortgage valuation using reduced-form model. Real Estate Economics, 36, 313–347.CrossRefGoogle Scholar
Milevsky, M.A. and Promislow, S.D. (2001) Mortality derivatives and the option to annuitise. Insurance: Mathematics and Economics, 29, 299–318.Google Scholar
Miltersen, K.R., Sandmann, K. and Sondermann, D. (1997) Closed form solutions for term structure derivatives with log-normal interest rate. Journal of Finance, 52, 409–430.Google Scholar
Quigley, J.M. and Van Order, R. (1990) Efficiency in the mortgage market: The Borrower's perspective. Journal of the AREUEA, 18, 237–252.Google Scholar
Quigley, J.M. and Van Order, R. (1995) Explicit tests of contingent claims models of mortgage default. The Journal of Real Estate Finance and Economics, 11, 99–117.Google Scholar
Schwartz, E.S. and Torous, W.N. (1989) Prepayment and the valuation of mortgage-backed securities. The Journal of Finance, 44, 375–392.Google Scholar
Schwartz, E.S. and Torous, W.N. (1992) Prepayment, default and the valuation of mortgage pass-through securities. Journal of Business, 65 (2), 221–239.CrossRefGoogle Scholar
Schwartz, E.S. and Torous, W.N. (1993) Mortgage prepayment and default decisions: A Poisson Regression approach. Journal of the AREUEA, 21, 431–449.Google Scholar
Stanton, R. (1995) Rational prepayment and the valuation of mortgage-backed securities. The Review of Financial Studies, 8, 677–708.Google Scholar