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Estimation of Housing Price Jump Risks and Their Impact on the Valuation of Mortgage Insurance Contracts

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  • Ming‐Chi Chen
  • Chia‐Chien Chang
  • Shih‐Kuei Lin
  • So‐De Shyu

Abstract

Housing price jump risk and the subprime crisis have drawn more attention to the precise estimation of mortgage insurance premiums. This study derives the pricing formula for mortgage insurance premiums by assuming that the housing price process follows the jump diffusion process, capturing important characteristics of abnormal shock events. This assumption is consistent with the empirical observation of the U.S. monthly national average new home returns from 1986 to 2008. Furthermore, we investigate the impact of price jump risk on mortgage insurance premiums from shock frequency of the abnormal events, abnormal mean and volatility of jump size, and normal volatility. Empirical results indicate that the abnormal volatility of jump size has the most significant impact on mortgage insurance premiums.

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  • 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.
    • Handle: RePEc:bla:jrinsu:v:77:y:2010:i:2:p:399-422
    DOI: 10.1111/j.1539-6975.2009.01326.x
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    Cited by:

    1. Gong, Xiaoye & Li, Ying & Wu, Yang-Che & Yang, Wan-Shiou, 2020. "Pricing various types of mortgage insurances with disposal and discount costs under a mean-reverting Lévy housing price process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    2. Ming Pu & Gang-Zhi Fan & Chunsheng Ban, 2016. "The Pricing of Mortgage Insurance Premiums Under Systematic and Idiosyncratic Shocks," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(2), pages 447-474, June.
    3. 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.
    4. Jr-Wei Huang & Sharon S. Yang & Chuang-Chang Chang, 2021. "Modeling Housing Price Dynamics and their Impact on the Cost of no-Negative-Equity-Guarantees for Equity Releasing Products," The Journal of Real Estate Finance and Economics, Springer, vol. 63(2), pages 249-279, August.
    5. Chia-Chien Chang & Min-Teh Yu, 2017. "Valuing Vulnerable Mortgage Insurance Under Capital Forbearance," The Journal of Real Estate Finance and Economics, Springer, vol. 54(4), pages 558-578, May.
    6. Oh, Sebeom & Ku, Hyejin & Jun, Doobae, 2022. "A comparative analysis of housing prices in different cities using the Black–Scholes and Jump Diffusion models," Finance Research Letters, Elsevier, vol. 46(PA).
    7. Calvo-Garrido, María del Carmen & Vázquez, Carlos, 2015. "Effects of jump-diffusion models for the house price dynamics in the pricing of fixed-rate mortgages, insurance and coinsurance," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 730-742.
    8. Poitras, Geoffrey & Zanotti, Giovanna, 2016. "Mortgage contract design and systemic risk immunization," International Review of Financial Analysis, Elsevier, vol. 45(C), pages 320-331.
    9. Wu, Yang-Che & Huang, Yi-Ting & Lin, Shih-Kuei & Chuang, Ming-Che, 2017. "Fair valuation of mortgage insurance under stochastic default and interest rates," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 433-447.
    10. Lee, Yung-Tsung & Wang, Chou-Wen & Huang, Hong-Chih, 2012. "On the valuation of reverse mortgages with regular tenure payments," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 430-441.
    11. 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.
    12. Katja Hanewald & Michael Sherris, 2011. "House Price Risk Models for Banking and Insurance Applications," Working Papers 201118, ARC Centre of Excellence in Population Ageing Research (CEPAR), Australian School of Business, University of New South Wales.
    13. 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.
    14. Lee, Yung-Tsung & Kung, Ko-Lun & Liu, I-Chien, 2018. "Profitability and risk profile of reverse mortgages: A cross-system and cross-plan comparison," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 255-266.

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