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Analytical solutions for expected and unexpected losses with an additional loan

Author

Listed:
  • Satoshi Yamashita

    (The Institute of Statistical Mathematics (E-mail: yamasita@ism.ac.jp))

  • Toshinao Yoshiba

    (Institute for Monetary and Economic Studies, Bank of Japan (E-mail: toshinao.yoshiba@boj.or.jp))

Abstract

We evaluate expected and unexpected losses of a bank loan, taking into account the bank fs strategic control of the expected return on the loan. Assuming that the bank supplies an additional loan to minimize the expected loss of the total loan, we provide analytical formulations for expected and unexpected losses with bivariate normal distribution functions.There are two cases in which an additional loan decreases the expected loss: i) the asset/liability ratio of the firm is low but its expected growth rate is high; ii) the asset/liability ratio of the firm is high and the lending interest rate is high. With a given expected growth rate and given interest rates, the two cases are identified by two thresholds for the current asset/liability ratio. The bank maintains the current loan amount when the asset/liability ratio is between the two thresholds. Given the bank fs strategy, the bank decreases the initial expected loss of the loan. On the other hand, the bank has a greater risk of the unexpected loss.

Suggested Citation

  • Satoshi Yamashita & Toshinao Yoshiba, 2007. "Analytical solutions for expected and unexpected losses with an additional loan," IMES Discussion Paper Series 07-E-21, Institute for Monetary and Economic Studies, Bank of Japan.
  • Handle: RePEc:ime:imedps:07-e-21
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    File URL: http://www.imes.boj.or.jp/research/papers/english/07-E-21.pdf
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    More about this item

    Keywords

    Probability of default (PD); Loss given default (LGD); Exposure at default (EaD); Expected loss (EL); Unexpected loss (UL); Stressed EL (SEL);

    JEL classification:

    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • G33 - Financial Economics - - Corporate Finance and Governance - - - Bankruptcy; Liquidation

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