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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.

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.

Suggested Citation

  • Mahayni, Antje & Schoenmakers, John G.M., 2011. "Minimum return guarantees with fund switching rights—An optimal stopping problem," Journal of Economic Dynamics and Control, Elsevier, vol. 35(11), pages 1880-1897.
  • Handle: RePEc:eee:dyncon:v:35:y:2011:i:11:p:1880-1897 DOI: 10.1016/j.jedc.2011.06.003
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    References listed on IDEAS

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    1. Goldbaum, David & Mizrach, Bruce, 2008. "Estimating the intensity of choice in a dynamic mutual fund allocation decision," Journal of Economic Dynamics and Control, Elsevier, vol. 32(12), pages 3866-3876, December.
    2. Carl Chiarella & Andrew Ziogas, 2009. "American Call Options Under Jump-Diffusion Processes - A Fourier Transform Approach," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(1), pages 37-79.
    3. Bergman, Yaacov Z & Grundy, Bruce D & Wiener, Zvi, 1996. " General Properties of Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1573-1610, December.
    4. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    5. Carl Chiarella & Boda Kang, 2009. "The Evaluation of American Compound Option Prices Under Stochastic Volatility Using the Sparse Grid Approach," Research Paper Series 245, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. T. F. Coleman & Y. Kim & Y. Li & M. Patron, 2007. "Robustly Hedging Variable Annuities With Guarantees Under Jump and Volatility Risks," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(2), pages 347-376.
    7. Chiarella, Carl & Ziogas, Andrew, 2005. "Evaluation of American strangles," Journal of Economic Dynamics and Control, Elsevier, pages 31-62.
    8. Brennan, Michael J. & Schwartz, Eduardo S., 1976. "The pricing of equity-linked life insurance policies with an asset value guarantee," Journal of Financial Economics, Elsevier, vol. 3(3), pages 195-213, June.
    9. Steven E. Shreve & Jan Vecer, 2000. "Options on a traded account: Vacation calls, vacation puts and passport options," Finance and Stochastics, Springer, vol. 4(3), pages 255-274.
    10. Nielsen, J. Aase & Sandmann, Klaus & Schlögl, Erik, 2011. "Equity-linked pension schemes with guarantees," Insurance: Mathematics and Economics, Elsevier, pages 547-564.
    11. 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.
    12. Harrison, J. Michael & Pliska, Stanley R., 1983. "A stochastic calculus model of continuous trading: Complete markets," Stochastic Processes and their Applications, Elsevier, vol. 15(3), pages 313-316, August.
    13. Boyle, Phelim P. & Hardy, Mary R., 1997. "Reserving for maturity guarantees: Two approaches," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 113-127, November.
    14. El Karoui, Nicole & Jeanblanc, Monique & Lacoste, Vincent, 2005. "Optimal portfolio management with American capital guarantee," Journal of Economic Dynamics and Control, Elsevier, vol. 29(3), pages 449-468, March.
    15. Tepla, Lucie, 2000. "Optimal portfolio policies with borrowing and shortsale constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1623-1639, October.
    16. Freddy Delbaen & Marc Yor, 2002. "Passport Options," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 299-328.
    17. Bacinello, Anna Rita & Ortu, Fulvio, 1993. "Pricing equity-linked life insurance with endogenous minimum guarantees : A corrigendum," Insurance: Mathematics and Economics, Elsevier, vol. 13(3), pages 303-304, December.
    18. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
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    Citations

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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. Antje Mahayni & Judith C. Schneider, 2016. "Minimum return guarantees, investment caps, and investment flexibility," Review of Derivatives Research, Springer, vol. 19(2), pages 85-111, July.
    3. Guo, Peijun & Li, Yonggang, 2014. "Approaches to multistage one-shot decision making," European Journal of Operational Research, Elsevier, vol. 236(2), pages 612-623.

    More about this item

    Keywords

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

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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