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Making Mean-Variance Hedging Implementable in a Partially Observable Market

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  • Masaaki Fujii

    (The University of Tokyo)

  • Akihiko Takahashi

    (The University of Tokyo)

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    Abstract

    The mean-variance hedging (MVH) problem is studied in a partially observable market where the drift processes can only be inferred through the observation of asset or index processes. Although most of the literatures treat the MVH problem by the duality method, here we study a system consisting of three BSDEs derived by Mania and Tevzadze (2003) and Mania et.al. (2008) and try to provide more explicit expressions directly implementable by practitioners. Under the Bayesian and Kalman-Bucy frameworks, we find that a relevant BSDE can yield a semi-closed solution via a simple set of ODEs which allow a quick numerical evaluation. This renders remaining problems equivalent to solving European contingent claims under a new forward measure, and it is straightforward to obtain a forward looking non-sequential Monte Carlo simulation scheme. We also give a special example where the hedging position is available in a semi-closed form. For more generic setups, we provide explicit expressions of approximate hedging portfolio by an asymptotic expansion. These analytic expressions not only allow the hedgers to update the hedging positions in real time but also make a direct analysis of the terminal distribution of the hedged portfolio feasible by standard Monte Carlo simulation.

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    File URL: http://www.carf.e.u-tokyo.ac.jp/pdf/workingpaper/fseries/F321.pdf
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    Bibliographic Info

    Paper provided by Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo in its series CARF F-Series with number CARF-F-321.

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    Length: 31 pages
    Date of creation: Jun 2013
    Date of revision:
    Handle: RePEc:cfi:fseres:cf321

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    References

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    1. Michael Mania & Marina Santacroce, 2010. "Exponential utility maximization under partial information," Finance and Stochastics, Springer, vol. 14(3), pages 419-448, September.
    2. Akihiko Takahashi & Kohta Takehara & Masashi Toda, 2012. "A General Computation Scheme For A High-Order Asymptotic Expansion Method," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(06), pages 1250044-1-1.
    3. Masaaki Fujii & Akihiko Takahashi, 2012. "ANALYTICAL APPROXIMATION FOR NON-LINEAR FBSDEs WITH PERTURBATION SCHEME," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(05), pages 1250034-1-1.
    4. Masaaki Fujii & Akihiko Takahashi, 2011. "Analytical Approximation for Non-linear FBSDEs with Perturbation Scheme," Papers 1106.0123, arXiv.org, revised Jan 2012.
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