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Multidimensional Breeden-Litzenberger representation for state price densities and static hedging

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  • Jarno Talponen
  • Lauri Viitasaari

Abstract

In this article, we consider European options of type $h(X^1_T, X^2_T,\ldots, X^n_T)$ depending on several underlying assets. We study how such options can be valued in terms of simple vanilla options in non-specified market models. We consider different approaches related to static hedging and derive several pricing formulas for a wide class of payoff functions $h:\R_+^n\rightarrow \R$. We also give new relations between prices of different options both in one dimensional and multidimensional case.

Suggested Citation

  • Jarno Talponen & Lauri Viitasaari, 2014. "Multidimensional Breeden-Litzenberger representation for state price densities and static hedging," Papers 1401.6383, arXiv.org.
  • Handle: RePEc:arx:papers:1401.6383
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    References listed on IDEAS

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    1. Brown, Donald J & Ross, Stephen A, 1991. "Spanning, Valuation and Options," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 3-12, January.
    2. Lauri Viitasaari, 2012. "Option prices with call prices," Papers 1207.6205, arXiv.org, revised Aug 2012.
    3. 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 621-651, October.
    4. Bick, Avi, 1982. "Comments on the valuation of derivative assets," Journal of Financial Economics, Elsevier, vol. 10(3), pages 331-345, November.
    5. Avi Bick., 1982. "Comments on the Valuation of Derivative Assets," Research Program in Finance Working Papers 125, University of California at Berkeley.
    6. Jarrow, Robert A., 1986. "A characterization theorem for unique risk neutral probability measures," Economics Letters, Elsevier, vol. 22(1), pages 61-65.
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