Duality and Derivative Pricing with Lévy Processes

Authors: José Fajardo and Ernesto Mordecki

Posted: 19/12/2003 (Final version). Status: Preprint

*Abstract:*
The aim of this work is to use a duality approach to study the
pricing of derivatives depending on
two stocks driven by a bidimensional Lévy process.
The main idea is to apply Girsanov's Theorem for Lévy processes,
in order to reduce the posed problem to the pricing of a one
Lévy driven stock in an auxiliary market, baptized as ``dual
market''. In this way, we extend the results obtained by Gerber
and Shiu (1996) for two dimensional Brownian motion. Also we
examine an existing relation between prices of put and call
options, of both the European and the American type. This
relation, based on a change of numeraire corresponding to a change
of the probability measure through Girsanov's Theorem, is
called * put - call duality*. It includes as a particular case, the
relation known as put - call symmetry. Necessary and sufficient
conditions for put - call symmetry to hold are obtained, in terms
of the triplet of predictable characteristic of the Lévy
process.

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[Articles by Ernesto Mordecki]