In this article , we consider European options of type h(X^1_T, X^2_T,\ldots, X^n_T) depending on many underlying assets. We study how such options can be valued in terms of simple vanilla options in different market models. We consider different approaches and derive several pricing formulas for a wide class of functions h:%DIFDELCMD < \R%%% _+^n\rightarrow%DIFDELCMD < \R%%% . We also give multidimensional version of the result of Breeden and Litzenberger Breeden on the relation between derivatives of the call price and the risk-neutral density of the underlying asset  .
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 %DIFDELCMD < \R%%% %DIFDELCMD < \R%%% give a multidimensional version of the result of Breeden and Litzenberger 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 .
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study how such options can be valued in terms of simple vanilla options in different market models. We consider different approaches and derive several pricing formulas for a wide class of functions h:
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