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An explicit formula for the chaotic representation of the powers ofincrements, (X_{t+t_0}-X_{t_0})^n, of a Levy process is presented. There aretwo different chaos expansions of a square integrable functional of a Levyprocess: one with respect to the compensated Poisson random measure and theother with respect to the orthogonal compensated powers of the jumps of theLevy process. Computationally explicit formulae for both of these chaosexpansions of (X_{t+t_0}-X_{t_0})^n are given in this paper. Simulation resultsverify that the representation is satisfactory. The CRP of a number offinancial derivatives can be found by expressing them in terms of(X_{t+t_0}-X_{t_0})^n using Taylor's expansion.

The Explicit Chaotic Representation of the powers of increments of Levy Processes