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Multivariate Option Pricing with Copulas

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Author Info

  • Umberto Cherubini
  • Elisa Luciano

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Abstract

In this paper we suggest the adoption of copula functions in order to price multivariate contingent claims. Copulas enable us to imbed the marginal distributions extracted from vertical spreads in the options markets in a multivariate pricing kernel. We prove that such kernel is a copula function, and that its super -replication strategy is represented by the Fréchet bounds. As applications, we provide prices for binary digital options, options on the minimum and options to exchange one asset for another. For each of these products, we provide no-arbitrage pricing bounds, as well as the values consistent with independence of the underlying assets. As a final reference value, we use a copula function calibrated on historical data.

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File URL: http://www.icer.it/docs/wp2002/luciano05-02.pdf
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Bibliographic Info

Paper provided by ICER - International Centre for Economic Research in its series ICER Working Papers - Applied Mathematics Series with number 05-2002.

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Length: 26 pages
Date of creation: Jan 2002
Date of revision:
Handle: RePEc:icr:wpmath:05-2002

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Related research

Keywords: option pricing; basket options; copula functions; non-normal returns;

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References

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  1. 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-.
  2. 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.
  3. Klein, Peter, 1996. "Pricing Black-Scholes options with correlated credit risk," Journal of Banking & Finance, Elsevier, vol. 20(7), pages 1211-1229, August.
  4. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
  5. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
  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.
  7. U. Cherubini & M. Esposito, 1995. "Options in and on interest rate futures contracts: results from martingale pricing theory," Applied Mathematical Finance, Taylor and Francis Journals, vol. 2(1), pages 1-16.
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