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Bivariate option pricing with copulas

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Author Info

  • U. Cherubini
  • E. Luciano

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 Frechet 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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File URL: http://www.tandfonline.com/doi/abs/10.1080/13504860210136721a
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Bibliographic Info

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

Volume (Year): 9 (2002)
Issue (Month): 2 ()
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

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  1. Klein, Peter, 1996. "Pricing Black-Scholes options with correlated credit risk," Journal of Banking & Finance, Elsevier, vol. 20(7), pages 1211-1229, August.
  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-.
  3. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
  4. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-51, October.
  5. 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.
  6. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
  7. 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.
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