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Minimum return guarantees with fund switching rights—An optimal stopping problem

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  • Mahayni, Antje
  • Schoenmakers, John G.M.
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    Abstract

    Recently, there is a growing trend to offer guaranteed products where the investor is allowed to shift her account/investment value between multiple funds. The switching right is granted a finite number of times per year, i.e. it is American style with multiple exercise possibilities. In consequence, the pricing and the risk management is based on the switching strategy which maximizes the value of the guarantee put-option. We analyze the optimal stopping problem in the case of one switching right within different model classes and compare the exact price with the lower price bound implied by the optimal deterministic switching time. We show that, within the class of log-price processes with independent increments, the stopping problem is solved by a deterministic stopping time if (and only if) the price process is in addition continuous. Thus, in a sense, the Black and Scholes model is the only (meaningful) pricing model where the lower price bound gives the exact price. It turns out that even moderate deviations from the Black and Scholes model assumptions give a lower price bound which is really below the exact price. This is illustrated by means of a stylized stochastic volatility model setup.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

    Volume (Year): 35 (2011)
    Issue (Month): 11 ()
    Pages: 1880-1897

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    Handle: RePEc:eee:dyncon:v:35:y:2011:i:11:p:1880-1897

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    Web page: http://www.elsevier.com/locate/jedc

    Related research

    Keywords: Return guarantees; Fund switching rights; Optimal stopping; American compound option;

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    References

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    1. J. Aase Nielsen & Klaus Sandmann & Erik Schlogl, 2010. "Equity-Linked Pension Schemes with Guarantees," Research Paper Series 270, Quantitative Finance Research Centre, University of Technology, Sydney.
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    Cited by:
    1. Mahayni, Antje & Schneider, Judith C., 2012. "Variable annuities and the option to seek risk: Why should you diversify?," Journal of Banking & Finance, Elsevier, vol. 36(9), pages 2417-2428.
    2. Guo, Peijun & Li, Yonggang, 2014. "Approaches to multistage one-shot decision making," European Journal of Operational Research, Elsevier, vol. 236(2), pages 612-623.
    3. Ankirchner, Stefan & Schneider, Judith C. & Schweizer, Nikolaus, 2014. "Cross-hedging minimum return guarantees: Basis and liquidity risks," Journal of Economic Dynamics and Control, Elsevier, vol. 41(C), pages 93-109.

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