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Liquidity and credit risk

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  • Umberto Cherubini
  • Giovanni Della Lunga

Abstract

The paper uses fuzzy measure theory to represent liquidity risk, i.e. the case in which the probability measure used to price contingent claims is not known precisely. This theory enables one to account for different values of long and short positions. Liquidity risk is introduced by representing the upper and lower bound of the price of the contingent claim computed as the upper and lower Choquet integral with respect to a subadditive function. The use of a specific class of fuzzy measures, known as g λ measures enables one to easily extend the available asset pricing models to the case of illiquid markets. As the technique is particularly useful in corporate claims evaluation, a fuzzified version of Merton's model of credit risk is presented. Sensitivity analysis shows that both the level and the range (the difference between upper and lower bounds) of credit spreads are positively related to the 'quasi debt to firm value ratio' and to the volatility of the firm value. This finding may be read as correlation between credit risk and liquidity risk, a result which is particularly useful in concrete risk-management applications. The model is calibrated on investment grade credit spreads, and it is shown that this approach is able to reconcile the observed credit spreads with risk premia consistent with observed default rate. Default probability ranges, rather than point estimates, seem to play a major role in the determination of credit spreads.

Suggested Citation

  • Umberto Cherubini & Giovanni Della Lunga, 2001. "Liquidity and credit risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(2), pages 79-95.
    • Handle: RePEc:taf:apmtfi:v:8:y:2001:i:2:p:79-95
    DOI: 10.1080/13504860110061013
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    References listed on IDEAS

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    Cited by:

    1. Mei Cai & Li Yan & Zaiwu Gong & Guo Wei, 2021. "A Voting Mechanism Designed for Talent Shows in Mass Media: Weighted Preference of Group Decision Makers in Social Networks Using Fuzzy Measures and Choquet Integral," Group Decision and Negotiation, Springer, vol. 30(6), pages 1261-1284, December.
    2. Muzzioli, S. & Torricelli, C., 2005. "The pricing of options on an interval binomial tree. An application to the DAX-index option market," European Journal of Operational Research, Elsevier, vol. 163(1), pages 192-200, May.
    3. Hertrich, Markus, 2015. "Does Credit Risk Impact Liquidity Risk? Evidence from Credit Default Swap Markets," MPRA Paper 67837, University Library of Munich, Germany.
    4. Umberto Cherubini & Elisa Luciano, 2003. "Pricing Vulnerable Options With Copulas," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 5(1), pages 27-39, April.
    5. Jia-wen Zhang & Long-hui Chen & Xiang-yun Liu & Fen Ding, 2014. "Measurement of Credit Risk of Small and Medium-sized S&T Enterprises in China," International Journal of Business Administration, International Journal of Business Administration, Sciedu Press, vol. 5(4), pages 21-31, July.
    6. Matthew Pritsker, 2005. "Large investors: implications for equilibrium asset, returns, shock absorption, and liquidity," Finance and Economics Discussion Series 2005-36, Board of Governors of the Federal Reserve System (U.S.).

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