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Note on multidimensional Breeden-Litzenberger representation for state price densities

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  • Jarno Talponen
  • Lauri Viitasaari

Abstract

In this note, we consider European options of type $h(X^1_T, X^2_T,\ldots, X^n_T)$ depending on several underlying assets. We give a multidimensional version of the result of Breeden and Litzenberger \cite{Breeden} on the relation between derivatives of the call price and the risk-neutral density of the underlying asset. The pricing measure is assumed to be absolutely continuous with respect to the Lebesgue measure on the state space.

Suggested Citation

  • Jarno Talponen & Lauri Viitasaari, 2013. "Note on multidimensional Breeden-Litzenberger representation for state price densities," Papers 1305.5963, arXiv.org, revised Jan 2014.
    • Handle: RePEc:arx:papers:1305.5963
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    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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    Cited by:

    1. Carlo Marinelli, 2024. "On certain representations of pricing functionals," Annals of Finance, Springer, vol. 20(1), pages 91-127, March.
    2. Carlo Marinelli, 2021. "On certain representations of pricing functionals," Papers 2109.05564, arXiv.org.
    3. Jonathan Ansari & Eva Lutkebohmert & Ariel Neufeld & Julian Sester, 2022. "Improved Robust Price Bounds for Multi-Asset Derivatives under Market-Implied Dependence Information," Papers 2204.01071, arXiv.org, revised Sep 2023.
    4. Hassane Abba Mallam & Diakarya Barro & Yameogo WendKouni & Bisso Saley, 2021. "Pricing multivariate european equity option using gaussian mixture distributions and evt-based copulas," Papers 2105.10599, arXiv.org.
    5. Jonathan Ansari & Eva Lütkebohmert & Ariel Neufeld & Julian Sester, 2024. "Improved robust price bounds for multi-asset derivatives under market-implied dependence information," Finance and Stochastics, Springer, vol. 28(4), pages 911-964, October.

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