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Note on multidimensional Breeden–Litzenberger representation for state price densities


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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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).

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

JEL Classification

  • G13
  • C02