Pricing Derivatives on Two Lévy-driven Stocks
AbstractThe aim of this work is to study the pricing problem for derivatives depending on two stocks driven by a bidimensional LÃ©vy process. The main idea is to apply Girsanov's Theorem for LÃ©vy processes, in order to reduce the posed problem to the pricing of a one LÃ©vy 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 LÃ©vy process
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Bibliographic InfoPaper provided by Finance Lab, Insper Instituto de Ensino e Pesquisa in its series Finance Lab Working Papers with number flwp_56.
Date of creation: Oct 2003
Date of revision:
Other versions of this item:
- Ernesto Mordecki & José Fajardo, 2004. "Pricing Derivatives on Two Lé}vy-driven Stocks," Econometric Society 2004 North American Winter Meetings 139, Econometric Society.
- 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-2003-10-20 (All new papers)
- NEP-FIN-2003-10-20 (Finance)
- NEP-FMK-2003-10-20 (Financial Markets)
- NEP-RMG-2003-10-20 (Risk Management)
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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- Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
- S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14.
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