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Liquidity and credit risk

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Author Info
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.

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

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

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

References listed on IDEAS
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. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March. [Downloadable!] (restricted)
  2. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April. [Downloadable!] (restricted)
  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. Merton, Robert C., 1973. "On the pricing of corporate debt: the risk structure of interest rates," Working papers 684-73., Massachusetts Institute of Technology (MIT), Sloan School of Management. [Downloadable!]
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  5. 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. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
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Cited by:
(explanations, 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. Umberto Cherubini & Elisa Luciano, 2002. "Pricing Vulnerable Options with Copulas," ICER Working Papers - Applied Mathematics Series 06-2002, ICER - International Centre for Economic Research. [Downloadable!]
  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.). [Downloadable!]
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