Symmetry and duality in Levy markets

José Fajardo () and Ernesto Mordecki

Quantitative Finance, 2006, vol. 6, issue 3, 219-227

Abstract: The aim of this paper is to introduce the notion of symmetry in a Levy 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, which is also reviewed in the paper, and that we call put-call duality. Symmetric Levy 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 Levy process, answering a question raised by Carr and Chesney (American put call symmetry, preprint, 1996). Some empirical evidence is shown, supporting that, in general, markets are not symmetric.

Keywords: Levy processes; Girsanov theorem; Smile; Numeraire; Duality; Symmetry (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (28)

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DOI: 10.1080/14697680600680068

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