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Weak Convergence of Hedging Strategies of Contingent Claims

  • Jean-Luc PRIGENT

    (Thema, Université de Cergy-Pontoise)

  • Olivier SCAILLET

    (HEC Genève and FAME)

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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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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  1. Schweizer, Martin, 1992. "Martingale densities for general asset prices," Journal of Mathematical Economics, Elsevier, vol. 21(4), pages 363-378.
  2. Olivier Renault & Jean-Luc Prigent & Olivier Scaillet, 2000. "An Autoregressive Conditional Binomial Option Pricing Model," FMG Discussion Papers dp364, Financial Markets Group.
  3. Schweizer, Martin, 1991. "Option hedging for semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 339-363, April.
  4. 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.
  5. J.L. Prigent & O. Renault & O. Scaillet., 1999. "Option pricing with discrete rebalancing," THEMA Working Papers 99-41, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  6. Runggaldier, Wolfgang J. & Martin Schweizer, 1995. "Convergence of Option Values under Incompleteness," Discussion Paper Serie B 333, University of Bonn, Germany.
  7. 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.
  8. repec:cup:cbooks:9780521335614 is not listed on IDEAS
  9. repec:fth:inseep:9961 is not listed on IDEAS
  10. Duffie, Darrell & Lando, David, 2001. "Term Structures of Credit Spreads with Incomplete Accounting Information," Econometrica, Econometric Society, vol. 69(3), pages 633-64, May.
  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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