Hurdle Rate: Executive Stock Options

Abstract

Executive stock options with a rising strike price are a recent innovation in executive compensation in Australia and New Zealand. These options combine a dividend protection feature and a strike price that increases at a hurdle rate set with reference to a cost of capital estimate. With a constant dividend yield, the strike price becomes a path-dependent function of the stock price and exact analytic valuation becomes intractable. However, path-dependent American options can be valued using a Monte Carlo approach proposed in Longstaff and Schwartz (2001). We examine procedures for valuing these options and compare them with Black and Scholes (1973) and Merton (1973) formula valuations.

Valuation and incentive effects of hurdle rate executive stock options

“…Integrating the two approaches provides a means for a comprehensive evaluation of hurdle rate ESOs hitherto unexamined. Cheung et al (2006) study has established that the modified Black-Scholes formula generally understates the risk-neutral value of a hurdle rate ESO, it does not address the issue that risk-neutral valuation overstates the objective cost to the firm of granting the option. This is because the risk-neutral value is calculated under the assumption of an optimal exercise strategy, while the constrained executive is likely to follow a suboptimal exercise policy.…”

“…2.1 Black-Scholes value of hurdle rate executive stock options (ESOs) Cheung et al (2006) appears to be the first study to examine valuation issues related to hurdle rate ESOs. They demonstrate that severe valuation biases may arise from the common approach of using a modified version of the option pricing formula of Black and Scholes (1973) to value hurdle rate ESOs.…”

“…This path dependency and the possibility of early exercise make exact analytic valuation of hurdle rate ESOs intractable. To handle this problem, Cheung et al (2006) estimate the risk-neutral value of hurdle rate options using the least squares Monte Carlo Valuation and incentive effects 271 (LSM) approach proposed by Longstaff and Schwartz (2001), which can accommodate valuation of path-dependent options. They find that the modified Black-Scholes option pricing formula typically understates severely the risk-neutral value of hurdle rate options.…”

The cost of granting executive stock options with strike prices adjusted by the cost of capital

“…The Cheung et al (2006) study Cheung et al (2006) investigate valuation biases that may arise from the common approach of using a modified version of option pricing formulas developed in Black and Scholes (1973) and Merton (1973) to value performance options. The modified Black-Scholes-Merton formula used is: Equation 1…”

“…Second, if a subjective valuation of the option is desired, path-dependency of the strike price means that standard valuation approaches, such as the use of utility functions in a binomial tree setting, would be impractical. Cheung et al (2006) tackle the first challenge by using the least squares Monte Carlo method developed in Longstaff and Schwartz (2001) to estimate the market value of performance options. We outline the least squares Monte Carlo methodology in Section 2.…”