Note on multidimensional Breeden-Litzenberger representation for state price densities

Jarno Talponen and Lauri Viitasaari

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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 \cite{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.

Date: 2013-05, Revised 2014-01
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Published in Mathematics and Financial Economics 8:153-157, 2014

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