Convergence of Option Values under Incompleteness
AbstractWe study the problem of convergence of discrete-time option values to continuous-time option values. While previous papers typically concentrate on the approximation of geometric Brownian motion by a binomial tree, we consider here the case where the model is incomplete in both continuos and discrete time. Option values are defined with respect to the criterion of local risk-minimization and thus computed as expectations under the respective minimal martingale measures. We prove that for a jump-diffusion model with deterministic coefficients, these values converge; this shows that local risk-minimization processes an inherent stability property under discretization.
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Bibliographic InfoPaper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 333.
Date of creation: 1995
Date of revision:
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option pricing; incomplete markets; convergence; minimal martingale measure; locally risk-minimization trading strategies; jump-diffusion;
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- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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- Prigent, J.-L. & Renault, O. & Scaillet, O., 1999.
"Option Pricing with Discrete Rebalancing,"
Discussion Papers (IRES - Institut de Recherches Economiques et Sociales)
1999029, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES), revised 00 Oct 1999.
- Jean -Luc Prigent & Olivier Renault & Olivier Scaillet, 1999. "Option Pricing with Discrete Rebalancing," Working Papers 99-61, Centre de Recherche en Economie et Statistique.
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- Jean-Luc PRIGENT & Olivier RENAULT & Olivier SCAILLET, 2002. "Option Pricing with Discrete Rebalancing," FAME Research Paper Series rp55, International Center for Financial Asset Management and Engineering.
- Jean-Luc PRIGENT & Olivier SCAILLET, 2002.
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- J.L. Prigent & O. Scaillet, 2000. "Weak Convergence of Hedging Strategies of Contingent Claims," THEMA Working Papers 2000-50, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
- Mulinacci, Sabrina, 1996. "An approximation of American option prices in a jump-diffusion model," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 1-17, March.
- Mercurio, Fabio, 2001. "Claim pricing and hedging under market incompleteness and "mean-variance" preferences," European Journal of Operational Research, Elsevier, vol. 133(3), pages 635-652, September.
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