Duality and Derivative Pricing with Lévy Processes
AbstractThe 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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Bibliographic InfoPaper provided by Economics Research Group, IBMEC Business School - Rio de Janeiro in its series IBMEC RJ Economics Discussion Papers with number 2005-01.
Date of creation: 25 Nov 2005
Date of revision:
Lévy processes; Optimal stopping; Girsanov's Theorem; Dual Market Method; Derivative pricing; Symmetry;
Other versions of this item:
- Fajardo, J. & Mordeckiz, E., 2004. "Duality and Derivative Pricing with Lévy Processes," Finance Lab Working Papers flwp_71, Finance Lab, Insper Instituto de Ensino e Pesquisa.
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-12-09 (All new papers)
- NEP-FIN-2005-12-09 (Finance)
- NEP-FMK-2005-12-09 (Financial Markets)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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