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We give the closed form of the ruin probability for a Lévy processes, possibly killed at a constant rate, with completely arbitrary positive distributed jumps, and finite intensity negative jumps with distribution characterized by having a rational Laplace or Fourier transform.Abbreviated Title: WH-factors of Lévy processes with rational jumps.

The aim of this paper is to introduce the notion of symmetry in a Lévy market. This notion appears as a particular case of a general known relation between prices of put and call options, of both the European and the American type, that is also reviewed in the paper, and that we call put-call duality. Symmetric Lévy markets have the distinctive feature of producing symmetric smile curves, in the log of strike/futures prices.Put-Call Duality is obtained as a consequence of a change of the risk neutral probability measure through Girsanov's Theorem, when considering the discounted and reinvested stock price as the numeraire. Symmetry is defined when a certain law before and after the change of measure through Girsanov's Theorem coincides. A parameter characterizing the departure from symmetry is introduced, and a necessary and sufficient condition for symmetry to hold is obtained, in terms of the jump measure of the Lévy process, answering a question raised by Carr and Chesney (1996). Some empirical evidence is shown, supporting that in general markets are not symmetric.