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Optimal multiple stopping models of reload options and shout options

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  • Dai, Min
  • Kwok, Yue Kuen

Abstract

The reload provision in an employee stock option entitles its holder to receive one new (reload) option from the employer for each share tendered as the payment of strike upon the exercise of the stock option. The number of reloads allowed can be finite or infinite. The shout feature in a call option allows its holder to reset the option's strike price to the prevailing stock price upon shouting. We explore a symmetry relationship between the price functions of the employee reload options and shout call options. When the dividend yield of the underlying stock is zero, the value of the employee reload option can be expressed in terms of the price functions of a shout call option and a forward contract. For an employee reload option with an infinite number of allowable reloads, the payoff of the employee reload option can be related to the lookback feature of the stock price process. We also examine the optimal exercise policies of the multi-reload employee stock options. The behavior of the critical stock price at which the holder should exercise optimally is shown to depend on the relative magnitude of the dividend yield, interest rate and volatility. Our analysis of the multi-reload and multi-shout options contributes to the literature on optimal stopping policies of contingent claims with multiple stopping rights.

Suggested Citation

  • Dai, Min & Kwok, Yue Kuen, 2008. "Optimal multiple stopping models of reload options and shout options," Journal of Economic Dynamics and Control, Elsevier, vol. 32(7), pages 2269-2290, July.
  • Handle: RePEc:eee:dyncon:v:32:y:2008:i:7:p:2269-2290
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    References listed on IDEAS

    as
    1. Philip H. Dybvig & Mark Loewenstein, 2003. "Employee Reload Options: Pricing, Hedging, and Optimal Exercise," The Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 145-171.
    2. Min Dai & Yue Kuen Kwok & Li Xin Wu, 2003. "Options with Multiple Reset Rights," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(06), pages 637-653.
    3. Johnson, Shane A. & Tian, Yisong S., 2000. "The value and incentive effects of nontraditional executive stock option plans," Journal of Financial Economics, Elsevier, vol. 57(1), pages 3-34, July.
    4. Alfredo Ibáñez, 2004. "Valuation by Simulation of Contingent Claims with Multiple Early Exercise Opportunities," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 223-248, April.
    5. Min Dai & Yue Kuen Kwok & Lixin Wu, 2004. "Optimal Shouting Policies Of Options With Strike Reset Right," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 383-401, July.
    6. Steven Huddart & Ravi Jagannathan & Jane Saly, 1999. "Valuing the Reload Features of Executive Stock Options," NBER Working Papers 7020, National Bureau of Economic Research, Inc.
    7. Min Dai & Yue Kuen Kwok, 2005. "Valuing employee reload options under the time vesting requirement," Quantitative Finance, Taylor & Francis Journals, vol. 5(1), pages 61-69.
    8. N. Meinshausen & B. M. Hambly, 2004. "Monte Carlo Methods For The Valuation Of Multiple‐Exercise Options," Mathematical Finance, Wiley Blackwell, vol. 14(4), pages 557-583, October.
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    Cited by:

    1. Tim Leung & Kazutoshi Yamazaki & Hongzhong Zhang, 2015. "Optimal Multiple Stopping with Negative Discount Rate and Random Refraction Times under Levy Models," Papers 1505.07313, arXiv.org.
    2. Nikolai Dokuchaev, 2010. "Controlled options: derivatives with added flexibility," Papers 1012.1412, arXiv.org, revised Oct 2011.
    3. Min Dai & Zuo Quan Xu, 2009. "Optimal Redeeming Strategy of Stock Loans," Papers 0906.0702, arXiv.org.
    4. Tim Leung & Kazutoshi Yamazaki & Hongzhong Zhang, 2015. "An Analytic Recursive Method For Optimal Multiple Stopping: Canadization And Phase-Type Fitting," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(05), pages 1-31.
    5. Cai, Ning & Sun, Lihua, 2014. "Valuation of stock loans with jump risk," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 213-241.

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