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Liquidity and credit risk

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  • Umberto Cherubini
  • Giovanni Della Lunga
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    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.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/13504860110061013
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    Bibliographic Info

    Article provided by Taylor and Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 8 (2001)
    Issue (Month): 2 ()
    Pages: 79-95
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    Handle: RePEc:taf:apmtfi:v:8:y:2001:i:2:p:79-95

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    For corrections or technical questions regarding this item, or to correct its listing, contact: (Michael McNulty).

    Related research

    Keywords: Credit Risk; Incomplete Markets; Liquidity Risk; Knightian Uncertainty; Option Pricing; Fuzzy Measures;

    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    1. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-70, May.
    2. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
    3. Camerer, Colin & Weber, Martin, 1992. " Recent Developments in Modeling Preferences: Uncertainty and Ambiguity," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 325-70, October.
    4. Marco Avellaneda & Antonio ParAS, 1996. "Managing the volatility risk of portfolios of derivative securities: the Lagrangian uncertain volatility model," Applied Mathematical Finance, Taylor and Francis Journals, vol. 3(1), pages 21-52.
    5. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    6. Boyle, Phelim P & Vorst, Ton, 1992. " Option Replication in Discrete Time with Transaction Costs," Journal of Finance, American Finance Association, vol. 47(1), pages 271-93, March.
    7. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
    8. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor and Francis Journals, vol. 2(2), pages 73-88.
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    Citations

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    Cited by:
    1. Umberto Cherubini & Elisa Luciano, 2002. "Pricing Vulnerable Options with Copulas," ICER Working Papers - Applied Mathematics Series 06-2002, ICER - International Centre for Economic Research.
    2. 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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