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Note on multidimensional Breeden–Litzenberger representation for state price densities

Mathematics and Financial Economics volume 8, pages 153–157 (2014)Cite this article

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 (J Bus 51:621–651, 1978) 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.

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Authors and Affiliations

  1. Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, 80101 , Joensuu, Finland

    Jarno Talponen

  2. Department of Mathematics and System Analysis, Aalto University, P.O. Box 11100, 00076 , Aalto, Finland

    Lauri Viitasaari

Authors
  1. Jarno Talponen
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  2. Lauri Viitasaari
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Correspondence to Jarno Talponen.

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Talponen, J., Viitasaari, L. Note on multidimensional Breeden–Litzenberger representation for state price densities. Math Finan Econ 8, 153–157 (2014). https://doi.org/10.1007/s11579-014-0113-5

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  • DOI: https://doi.org/10.1007/s11579-014-0113-5

Keywords

  • Option valuation
  • Options of multidimensional assets
  • State price densities
  • Rainbow options
  • Basket options
  • Breeden–Litzenberger representation

JEL Classification

  • G13
  • C02