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Note on multidimensional Breeden–Litzenberger representation for state price densities

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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

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  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

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