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Discrete-Time Variance-Optimal Hedging In Affine Stochastic Volatility Models

In: Alternative Investments And Strategies

Author

Listed:
  • JAN KALLSEN

    (Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Christian-Albrechts Platz 4, 24098 Kiel, Germany)

  • JOHANNES MUHLE-KARBE

    (Fakultät für Mathematik, Universität Wien, Austria Nordbergstr. 15, 1090 Wien, Austria)

  • NATALIA SHENKMAN

    (Lehrstuhl für Energiehandel und Finanzdienstleistungen, Universität Duisburg-Essen, Universitätsstraße 12, 45141 Essen, Germany)

  • RICHARD VIERTHAUER

    (Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Christian-Albrechts Platz 4, 24098 Kiel, Germany)

Abstract

We consider variance-optimal hedging when trading is restricted to a finite time set. Using Laplace transform methods, we derive semi-explicit formulas for the variance-optimal initial capital and hedging strategy in affine stochastic volatility models. For the corresponding minimal expected-squared hedging error, we propose a closed-form approximation as well as a simulation approach. The results are illustrated by computing the relevant quantities in a time-changed Lévy model.

Suggested Citation

  • Jan Kallsen & Johannes Muhle-Karbe & Natalia Shenkman & Richard Vierthauer, 2010. "Discrete-Time Variance-Optimal Hedging In Affine Stochastic Volatility Models," World Scientific Book Chapters, in: Rüdiger Kiesel & Matthias Scherer & Rudi Zagst (ed.), Alternative Investments And Strategies, chapter 15, pages 375-393, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789814280112_0015
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    Citations

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    Cited by:

    1. Jakub Trybuła & Dariusz Zawisza, 2019. "Continuous-Time Portfolio Choice Under Monotone Mean-Variance Preferences—Stochastic Factor Case," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 966-987, August.
    2. Augustyniak, Maciej & Badescu, Alexandru & Bégin, Jean-François, 2023. "A discrete-time hedging framework with multiple factors and fat tails: On what matters," Journal of Econometrics, Elsevier, vol. 232(2), pages 416-444.

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