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Bivariate option pricing with copulas

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Author Info
U. Cherubini
E. Luciano

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Abstract

The adoption of copula functions is suggested in order to price bivariate contingent claims. Copulas enable the marginal distributions extracted from vertical spreads in the options markets to be imbedded in a multivariate pricing kernel. It is proved that such a kernel is a copula function, and that its super-replication strategy is represented by the Fre´chet bounds. Applications provided include prices for binary digital options, options on the minimum and options to exchange one asset for another. For each of these products, no-arbitrage pricing bounds, as well as values consistent with the independence of the underlying assets are provided. As a final reference value, a copula function calibrated on historical data is used.

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

Volume (Year): 9 (2002)
Issue (Month): 2 (June)
Pages: 69-85
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Handle: RePEc:taf:apmtfi:v:9:y:2002:i:2:p:69-85

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Related research
Keywords: Bivariate Option Pricing; Copula Functions; Pricing Kernel; Applications;

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. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July. [Downloadable!] (restricted)
  2. Joshua Rosenberg, 1999. "Semiparametric Pricing of Multivariate Contingent Claims," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-028, New York University, Leonard N. Stern School of Business-. [Downloadable!]
  3. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," Journal of Business, University of Chicago Press, vol. 51(4), pages 621-51, October. [Downloadable!] (restricted)
  4. Klein, Peter, 1996. "Pricing Black-Scholes options with correlated credit risk," Journal of Banking & Finance, Elsevier, vol. 20(7), pages 1211-1229, August. [Downloadable!] (restricted)
  5. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley. [Downloadable!]
  6. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-86, March. [Downloadable!] (restricted)
  7. Stulz, ReneM., 1982. "Options on the minimum or the maximum of two risky assets : Analysis and applications," Journal of Financial Economics, Elsevier, vol. 10(2), pages 161-185, July. [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. Dominique Guegan & Jing Zhang, 2009. "Pricing bivariate option under GARCH-GH model with dynamic copula: application for Chinese market," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00368336_v1, HAL. [Downloadable!]
    Other versions:
  2. Xia Su, 2006. "Hedging Basket Options by Using a Subset of Underlying Assets," Bonn Econ Discussion Papers bgse14_2006, University of Bonn, Germany. [Downloadable!]
  3. Elisa Luciano & Wim Schoutens, 2006. "A Multivariate Jump-Driven Financial Asset Model," Carlo Alberto Notebooks 29, Collegio Carlo Alberto. [Downloadable!]
    Other versions:
  4. Rob van den Goorbergh, 2004. "A Copula-Based Autoregressive Conditional Dependence Model of International Stock Markets," DNB Working Papers 022, Netherlands Central Bank, Research Department. [Downloadable!]
  5. Jing Zhang & Dominique Guegan, 2008. "Pricing bivariate option under GARCH processes with time-varying copula," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00286054_v1, HAL. [Downloadable!]
    Other versions:
  6. Oriol Roch Casellas & Antonio Alegre Escolano, 2005. "Testing the bivariate distribution of daily equity returns using copulas. An application to the Spanish stock market," Working Papers in Economics 143, Universitat de Barcelona. Espai de Recerca en Economia. [Downloadable!]
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