Note on multidimensional Breeden-Litzenberger representation for state price densities

摘要

In this note, we consider European optionsof type h(X_T~1, X_T~2,..., X_T~n) 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.