Valuation and incentive effects of hurdle rate executive stock options

Abstract

Traditional executive stock options are often criticized for inherently weak links between pay and performance. Hurdle rate executive stock options represent a viable improvement. However, valuing these options presents extraordinary analytic difficulties. With a constant dividend yield the strike price becomes a path-dependent function of the stock price and exact analytic valuation is intractable. To solve this problem, we apply the Monte Carlo valuation approach developed by Longstaff and Schwartz (Rev Financ Stud 4:113–147, 2001) to estimate the value of path-dependent American options. We also extend the methodology to incorporate the theoretical framework by Ingersoll (J Bus 79:453–487, 2006) to permit subjective valuation influenced by an executive’s risk aversion.

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Notes

  1. 1.

    For instance, companies on the Australian or New Zealand stock exchanges that have issued hurdle rate ESOs include Fisher and Paykel Appliances, Fisher and Paykel Healthcare, Fletcher Building, Macquarie Goodman Group, Pumpkin Patch Limited, Sky City Entertainment Group and others.

  2. 2.

    See page 50 in Fisher and Paykel Appliances Holdings Limited’s 2007 annual report available from www.fisherpaykel.com.

  3. 3.

    See page 46 in Fletcher Building’s 2007 annual report available from www.fletcherbuilding.co.nz.

  4. 4.

    Indeed, the least squares Monte Carlo approach is sufficiently flexible to account for a host of factors that might affect the value of executive stock options. For example, Carr and Linetsky (2000) and Szimayer (2004) examine changes in the payoff structure of executive stock options caused by the early departure of an executive or a company takeover. Szimayer (2005) examines the impact of event risk on executive stock option exercise strategies and option values in a general setting. In his model, the occurrence of an event terminates the option’s promised payoff schedule and is replaced with a rebate determined by the event. Default risk and career change are examples for this type of event. See, for example, Elliot et al. (2000), Bielecki and Rutkowski (2001), and Blanchet-Scalliet and Jeanblanc (2004).

  5. 5.

    Ingersoll (2006) uses a constant relative risk aversion utility function of the form: \( \frac{1} {{(1 - \alpha )}}{\int\limits_0^\infty {e^{{ - \rho t}} C^{{1 - \alpha }}_{t} dt} } \).

  6. 6.

    These are approximately the mean values used in Ingersoll (2006).

  7. 7.

    See, for instance, Ingersoll (2006) and Boyle and Scott (2006) for a discussion on problems related to such an ad hoc approach.

  8. 8.

    We can also consider the reciprocal of the unit cost of delta measure as the incentive strength per unit of compensation. It is clear in Table 6 that the hurdle rate ESO has a higher incentive strength per dollar cost than the standard ESO with a constant strike.

  9. 9.

    The firm could also choose the strike price. However, we maintain the assumption that an ESO is originally issued at the money with the initial strike price set to equal the current stock price, which is the norm for these ESOs.

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Correspondence to Charles Corrado.

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Cheung, J., Corrado, C. Valuation and incentive effects of hurdle rate executive stock options. Rev Quant Finan Acc 32, 269–285 (2009). https://doi.org/10.1007/s11156-008-0093-8

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Keywords

  • Executive stock options
  • Monte Carlo simulations
  • Hurdle rate

JEL Classifications

  • G12
  • G13
  • G32