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Weak Convergence of Hedging Strategies of Contingent Claims

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  • J.L. Prigent
  • O. Scaillet

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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  • 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.
    • Handle: RePEc:ema:worpap:2000-50
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    1. Duffie, Darrell & Lando, David, 2001. "Term Structures of Credit Spreads with Incomplete Accounting Information," Econometrica, Econometric Society, vol. 69(3), pages 633-664, May.
    2. Jean -Luc Prigent & Olivier Renault & Olivier Scaillet, 1999. "An Autoregressive Conditional Binomial Option Pricing Model," Working Papers 99-65, Center for Research in Economics and Statistics.
    3. 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.
    4. Prigent, Jean-Luc & Renault, Olivier & Scaillet, Olivier, 2004. "Option pricing with discrete rebalancing," Journal of Empirical Finance, Elsevier, vol. 11(1), pages 133-161, January.
    5. Runggaldier, Wolfgang J. & Martin Schweizer, 1995. "Convergence of Option Values under Incompleteness," Discussion Paper Serie B 333, University of Bonn, Germany.
    6. Schweizer, Martin, 1992. "Martingale densities for general asset prices," Journal of Mathematical Economics, Elsevier, vol. 21(4), pages 363-378.
    7. Schweizer, Martin, 1991. "Option hedging for semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 339-363, April.
    8. 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, October.
    9. Naoto Kunitomo & Masayuki Ikeda, 2000. "Correction: Pricing Options with Curved Boundaries (Mathematical Finance 1992, 2, 275–297)," Mathematical Finance, Wiley Blackwell, vol. 10(4), pages 459-459, October.
    10. repec:crs:wpaper:9961 is not listed on IDEAS
    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. Alexandre Adam & Hamza Cherrat & Mohamed Houkari & Jean-Paul Laurent & Jean-Luc Prigent, 2022. "On the risk management of demand deposits: quadratic hedging of interest rate margins," Annals of Operations Research, Springer, vol. 313(2), pages 1319-1355, June.
    2. 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.
    3. Badescu, Alexandru & Elliott, Robert J. & Ortega, Juan-Pablo, 2015. "Non-Gaussian GARCH option pricing models and their diffusion limits," European Journal of Operational Research, Elsevier, vol. 247(3), pages 820-830.
    4. 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.
    5. Maciej Augustyniak & Alexandru Badescu, 2021. "On the computation of hedging strategies in affine GARCH models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(5), pages 710-735, May.

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