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Conditional-Mean Hedging Under Transaction Costs In Gaussian Models

Author

Listed:
  • TOMMI SOTTINEN

    (Department of Mathematics and Statistics, University of Vaasa, Vaasa, P. O. Box 700, FIN-65101 Vaasa, Finland)

  • LAURI VIITASAARI

    (Department of Mathematics and System Analysis, Aalto University School of Science, Helsinki, P. O. Box 11100, FIN-00076 Aalto, Finland)

Abstract

We consider so-called regular invertible Gaussian Volterra processes and derive a formula for their prediction laws. Examples of such processes include the fractional Brownian motions and the mixed fractional Brownian motions. As an application, we consider conditional-mean hedging under transaction costs in Black–Scholes type pricing models where the Brownian motion is replaced with a more general regular invertible Gaussian Volterra process.

Suggested Citation

  • Tommi Sottinen & Lauri Viitasaari, 2018. "Conditional-Mean Hedging Under Transaction Costs In Gaussian Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-15, March.
    • Handle: RePEc:wsi:ijtafx:v:21:y:2018:i:02:n:s0219024918500152
    DOI: 10.1142/S0219024918500152
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    References listed on IDEAS

    as
    1. Tommi Sottinen & Lauri Viitasaari, 2016. "Stochastic Analysis of Gaussian Processes via Fredholm Representation," International Journal of Stochastic Analysis, Hindawi, vol. 2016, pages 1-15, July.
    2. Leland, Hayne E, 1985. "Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
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    4. Yuri Kabanov, 2009. "Markets with Transaction Costs. Mathematical Theory," Post-Print hal-00488168, HAL.
    5. Gapeev Pavel V. & Sottinen Tommi & Valkeila Esko, 2011. "Robust replication in H-self-similar Gaussian market models under uncertainty," Statistics & Risk Modeling, De Gruyter, vol. 28(1), pages 37-50, March.
    6. Emmanuel Denis & Yuri Kabanov, 2010. "Mean square error for the Leland–Lott hedging strategy: convex pay-offs," Finance and Stochastics, Springer, vol. 14(4), pages 625-667, December.
    7. Sottinen, Tommi & Viitasaari, Lauri, 2017. "Prediction law of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 155-166.
    8. Christian Bender & Tommi Sottinen & Esko Valkeila, 2008. "Pricing by hedging and no-arbitrage beyond semimartingales," Finance and Stochastics, Springer, vol. 12(4), pages 441-468, October.
    9. Christian Bender & Tommi Sottinen & Esko Valkeila, 2010. "Fractional processes as models in stochastic finance," Papers 1004.3106, arXiv.org.
    Full references (including those not matched with items on IDEAS)

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