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On the term structure of lending interest rates when a fraction of collateral is recovered upon default

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Abstract

This article provides an arbitrage-free model to evaluate the term structure of lending interest rates when a fraction of collateral is recovered upon default of the borrower. Unlike the previous literature, we assume that the value of the collateral asset fluctuates over time with certain correlation to the risk-free interest rate as well as the default hazard rate of the borrower. It is shown that the bank loan is a sum of holding a coupon-bearing bond and selling a put option, both being callable upon default. A Gaussian model is considered, as a special case, to derive an analytic expression of the appropriate lending interest rates, and some numerical example is given to demonstrate that bank loans exhibit different properties from corporate bonds.

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Authors and Affiliations

  1. Graduate School of Economics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, 606-8501, Kyoto, Japan

    Masaaki Kijima

  2. Credit Supervision Division, Bank of Kyoto, 700 Yakushimae-cho, Karasuma-dori, Shimogyo-ku, 600-8652, Kyoto, Japan

    Yusuke Miyake

Authors
  1. Masaaki Kijima
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  2. Yusuke Miyake
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Corresponding author

Correspondence to Masaaki Kijima.

Additional information

The authors are grateful to anonymous referees for invaluable comments that improved the original manuscript. Careful reading of the manuscript made by Katsumasa Nishide is also acknowledged. One of the authors (M.K.) acknowledges the financial support by Daiwa Securities Group Inc. Remaining errors are of course ours.

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Kijima, M., Miyake, Y. On the term structure of lending interest rates when a fraction of collateral is recovered upon default. Japan J. Indust. Appl. Math. 21, 35–56 (2004). https://doi.org/10.1007/BF03167431

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  • DOI: https://doi.org/10.1007/BF03167431

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