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Pricing Vulnerable Options With Copulas

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  • UMBERTO CHERUBINI
  • ELISA LUCIANO

Abstract

In this paper we apply a copula function pricing technique to the evaluation of vulnerable options, i.e. options with counterpart risk. Using copulas enables to separate the specification of marginal distributions and the dependence structure of the events of exercise of the option and default of the counterpart. Our proof that counterpart risk is evaluated as a copula function is based on no-arbitrage arguments only. This makes our results directly applicable to incomplete market models. Also, the no-arbitrage arguments provide easy-to-implement super-replication strategies. We study digital, call and put options with counterpart risk. Furtehr, we price a credit derivative contract, namely a default put option. We calibrate the models on real market data, using a mixing copula, which provides closed form pricing formulas.
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Suggested Citation

  • 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.
    • Handle: RePEc:eme:jrfpps:eb022977
    DOI: 10.1108/eb022977
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    1. is not listed on IDEAS
    2. Gajdos, Thibault & Tallon, Jean-Marc & Vergnaud, Jean-Christophe, 2004. "Decision making with imprecise probabilistic information," Journal of Mathematical Economics, Elsevier, vol. 40(6), pages 647-681, September.
    3. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On consistency of nonparametric normal mixtures for Bayesian density estimation," ICER Working Papers - Applied Mathematics Series 23-2004, ICER - International Centre for Economic Research.
    4. Renault, Jerome & Scarlatti, Sergio & Scarsini, Marco, 2005. "A folk theorem for minority games," Games and Economic Behavior, Elsevier, vol. 53(2), pages 208-230, November.
    5. Mjøs, Aksel & Persson, Svein-Arne, 2010. "A simple model of deferred callability in defaultable debt," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1350-1357, December.
    6. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On rates of convergence for posterior distributions in infinite–dimensional models," ICER Working Papers - Applied Mathematics Series 24-2004, ICER - International Centre for Economic Research.
    7. Salvatore Modica & Marco Scarsini, 2003. "The convexity-cone approach to comparative risk and downside risk," ICER Working Papers - Applied Mathematics Series 01-2003, ICER - International Centre for Economic Research.
    8. Taizhong Hu & Alfred Müller & Marco Scarsini, 2002. "Some Counterexamples in Positive Dependence," ICER Working Papers - Applied Mathematics Series 28-2003, ICER - International Centre for Economic Research, revised Jul 2003.
    9. Enrico Diecidue & Fabio Maccheroni, 2002. "Coherence without Additivity," ICER Working Papers - Applied Mathematics Series 10-2002, ICER - International Centre for Economic Research.
    10. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "Contributions to the understanding of Bayesian consistency," ICER Working Papers - Applied Mathematics Series 13-2004, ICER - International Centre for Economic Research.
    11. Gajdos, Thibault & Maurin, Eric, 2004. "Unequal uncertainties and uncertain inequalities: an axiomatic approach," Journal of Economic Theory, Elsevier, vol. 116(1), pages 93-118, May.
    12. Castagnoli, Erio & Maccheroni, Fabio & Marinacci, Massimo, 2002. "Insurance premia consistent with the market," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 267-284, October.
    13. Arismendi-Zambrano, Juan & Belitsky, Vladimir & Sobreiro, Vinicius Amorim & Kimura, Herbert, 2022. "The implications of dependence, tail dependence, and bounds’ measures for counterparty credit risk pricing," Journal of Financial Stability, Elsevier, vol. 58(C).
    14. Müller, Alfred & Scarsini, Marco, 2005. "Archimedean copulæ and positive dependence," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 434-445, April.

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