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Weak Convergence of Hedging Strategies of Contingent Claims

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  • Jean-Luc PRIGENT

    (Thema, Université de Cergy-Pontoise)

  • Olivier SCAILLET

    (HEC Genève and FAME)

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

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References

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  1. Runggaldier, Wolfgang J. & Martin Schweizer, 1995. "Convergence of Option Values under Incompleteness," Discussion Paper Serie B 333, University of Bonn, Germany.
  2. David Heath & Eckhard Platen & Martin Schweizer, 2001. "A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 385-413.
  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.
  4. Jean -Luc Prigent & Olivier Renault & Olivier Scaillet, 1999. "An Autoregressive Conditional Binomial Option Pricing Model," Working Papers 99-65, Centre de Recherche en Economie et Statistique.
  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. Jean-Philippe Lesne & Jean-Luc Prigent & Olivier Scaillet, 1998. "Convergence of Discrete Time Option Pricing Models Under Stochastic Interest Rates," Working Papers 98-51, Centre de Recherche en Economie et Statistique.
  7. Schweizer, Martin, 1991. "Option hedging for semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 339-363, April.
  8. repec:fth:inseep:9961 is not listed on IDEAS
  9. Debreu,Gerard Introduction by-Name:Hildenbrand,Werner, 1986. "Mathematical Economics," Cambridge Books, Cambridge University Press, number 9780521335614.
  10. Schweizer, Martin, 1992. "Martingale densities for general asset prices," Journal of Mathematical Economics, Elsevier, vol. 21(4), pages 363-378.
  11. 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.
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Cited by:
  1. Badescu, Alexandru & Elliott, Robert J. & Ortega, Juan-Pablo, 2014. "Quadratic hedging schemes for non-Gaussian GARCH models," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 13-32.
  2. Alexandru Badescu & Robert J. Elliott & Juan-Pablo Ortega, 2012. "Quadratic hedging schemes for non-Gaussian GARCH models," Papers 1209.5976, arXiv.org, revised Dec 2013.

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