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The Cost of Delay in a Mortgage/Credit Loan Portfolio

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  • Jang Jiwook

    (Macquarie University)

Abstract

Using an actuarial model, we examine the cost of delay in mortgage/credit loan payments. It is assumed that the default arrival process follows the Poisson process and the loss sizes are assumed to be independent and an identical truncated exponential. We also assume that the delay between default occurrence and partially (or fully) recovered payment is an independent identical truncated exponential random variable. For the recovery rate random variable, we simply use its expectation. Using the relationship between the shot noise process and accumulated/discounted aggregate losses process and applying the piecewise deterministic Markov processes theory, we obtain the explicit expressions for the expected value of losses and the expected value of part (or whole) of the loan recovered with the delay. Based on these moments, we define and predict the cost of delay in a mortgage/credit loan portfolio and their numerical examples are provided.

Suggested Citation

  • Jang Jiwook, 2009. "The Cost of Delay in a Mortgage/Credit Loan Portfolio," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 4(1), pages 1-14, November.
  • Handle: RePEc:bpj:apjrin:v:4:y:2009:i:1:n:5
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    References listed on IDEAS

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    1. Jang, Ji-Wook & Krvavych, Yuriy, 2004. "Arbitrage-free premium calculation for extreme losses using the shot noise process and the Esscher transform," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 97-111, August.
    2. Ji-Wook Jang, 2004. "Martingale Approach for Moments of Discounted Aggregate Claims," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 71(2), pages 201-211.
    3. Ambrose, Brent W & Buttimer, Richard J, Jr & Capone, Charles A, 1997. "Pricing Mortgage Default and Foreclosure Delay," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(3), pages 314-325, August.
    4. James B. Kau & Taewon Kim, 1994. "Waiting to Default: The Value of Delay," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 22(3), pages 539-551.
    5. Jang, Jiwook, 2007. "Jump diffusion processes and their applications in insurance and finance," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 62-70, July.
    6. Dassios, Angelos & Jang, Jiwook, 2003. "Pricing of catastrophe reinsurance and derivatives using the Cox process with shot noise intensity," LSE Research Online Documents on Economics 2849, London School of Economics and Political Science, LSE Library.
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