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Weak Convergence of Hedging Strategies of Contingent Claims

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Author Info
Jean-Luc PRIGENT (Thema, Université de Cergy-Pontoise)
Olivier SCAILLET (HEC Genève and FAME)

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Abstract

This paper presents results on the convergence for hedging strategies in the setting of incomplete financial markets. We examine the convergence of the so-called locally risk-minimizing strategy. It is proved that such a choice for the trading strategy, when perfect hedging of contingent claims is infeasible, is robust under weak convergence. Several fundamental examples, such as trinomial trees and stochastic volatility models, extracted from the financial modeling literature illustrate this property for both deterministic and random time intervals shrinking to zero.

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Publisher Info
Paper provided by International Center for Financial Asset Management and Engineering in its series FAME Research Paper Series with number rp39.

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Date of creation: Jan 2002
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Handle: RePEc:fam:rpseri:rp39

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Related research
Keywords: Weak convergence; Incomplete financial markets; Locally risk-minimizing strategy; Hedging strategy; Minimal martingale measure;

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References listed on IDEAS
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  1. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June. [Downloadable!] (restricted)
  2. O. Scaillet & J.-L. Prigent & J.-P. Lesne, 2000. "Convergence of discrete time option pricing models under stochastic interest rates," Finance and Stochastics, Springer, vol. 4(1), pages 81-93. [Downloadable!] (restricted)
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  3. 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. [Downloadable!]
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  4. Schweizer, Martin, 1992. "Martingale densities for general asset prices," Journal of Mathematical Economics, Elsevier, vol. 21(4), pages 363-378. [Downloadable!] (restricted)
  5. Duffie, Darrell & Lando, David, 2001. "Term Structures of Credit Spreads with Incomplete Accounting Information," Econometrica, Econometric Society, vol. 69(3), pages 633-64, May.
  6. Runggaldier, Wolfgang J. & Martin Schweizer, 1995. "Convergence of Option Values under Incompleteness," Discussion Paper Serie B 333, University of Bonn, Germany.
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