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Non Quadratic Local Risk-Minimization for Hedging Contingent Claims in the Presence of Transaction Costs

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  • Frédéric Abergel

    () (MAS - Mathématiques Appliquées aux Systèmes - EA 4037 - Ecole Centrale Paris, FiQuant - Chaire de finance quantitative - Ecole Centrale Paris)

  • Nicolas Millot

    (MAS - Mathématiques Appliquées aux Systèmes - EA 4037 - Ecole Centrale Paris, FiQuant - Chaire de finance quantitative - Ecole Centrale Paris)

Abstract

This paper is devoted to the study of derivative hedging in incomplete markets when frictions are considered. We extend the general local risk minimisation approach introduced in [1] to account for liquidity costs, and derive the corresponding optimal strategies in both the discrete- and continuous-time settings. We examplify our method in the case of stochastic volatility and/or jump-diffusion models.

Suggested Citation

  • Frédéric Abergel & Nicolas Millot, 2011. "Non Quadratic Local Risk-Minimization for Hedging Contingent Claims in the Presence of Transaction Costs," Working Papers hal-00621256, HAL.
  • Handle: RePEc:hal:wpaper:hal-00621256 Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00621256v2
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    1. 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.
    2. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters,in: Theory Of Valuation, chapter 8, pages 229-288 World Scientific Publishing Co. Pte. Ltd..
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    4. Föllmer, H. & Schweizer, M., 1989. "Hedging by Sequential Regression: an Introduction to the Mathematics of Option Trading," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 19(S1), pages 29-42, November.
    5. Umut Çetin & Robert A. Jarrow & Philip Protter, 2008. "Liquidity risk and arbitrage pricing theory," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 8, pages 153-183 World Scientific Publishing Co. Pte. Ltd..
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